diff --git a/lang/en/question.php b/lang/en/question.php
index 48b6a4b25cb..6c4c48dce0d 100644
--- a/lang/en/question.php
+++ b/lang/en/question.php
@@ -58,6 +58,7 @@ $string['cannotmovequestion'] = 'You can\'t use this script to move questions th
 $string['cannotopenforwriting'] = 'Cannot open for writing: {$a}';
 $string['cannotpreview'] = 'You can\'t preview these questions!';
 $string['cannotread'] = 'Cannot read import file (or file is empty)';
+$string['cannotregradedifferentqtype'] = 'Cannot regrade with a question of a different type.';
 $string['cannotretrieveqcat'] = 'Could not retrieve question category';
 $string['cannotunhidequestion'] = 'Failed to unhide the question.';
 $string['cannotunzip'] = 'Could not unzip file.';
diff --git a/mod/quiz/report/overview/lang/en/quiz_overview.php b/mod/quiz/report/overview/lang/en/quiz_overview.php
index 67024620999..852f6806877 100644
--- a/mod/quiz/report/overview/lang/en/quiz_overview.php
+++ b/mod/quiz/report/overview/lang/en/quiz_overview.php
@@ -63,11 +63,13 @@ $string['regradealldrydo'] = 'Regrade attempts marked as needing regrading ({$a}
 $string['regradealldrydogroup'] = 'Regrade attempts ({$a->countregradeneeded}) marked as needing regrading in group \'{$a->groupname}\'';
 $string['regradealldrygroup'] = 'Dry run a full regrade for group \'{$a->groupname}\'';
 $string['regradeallgroup'] = 'Full regrade for group \'{$a->groupname}\'';
-$string['regradecomplete'] = 'Regrade completed successfully';
-$string['regradedsuccessfullyxofy'] = 'Successfully regraded ({$a->done}/{$a->count})';
+$string['regradecomplete'] = 'Regrade completed';
+$string['regradedsuccessfullyxofy'] = 'Finished regrading ({$a->done}/{$a->count})';
 $string['regradeheader'] = 'Regrading';
 $string['regradeselected'] = 'Regrade selected attempts';
+$string['regradingattemptissue'] = 'Slot {$a->slot}: {$a->reason}';
 $string['regradingattemptxofy'] = 'Regrading attempt ({$a->done}/{$a->count})';
+$string['regradingattemptxofyproblem'] = 'The following questions could not be regraded in attempt {$a->attemptnum} by {$a->name} (id {$a->attemptid})';
 $string['regradingattemptxofywithdetails'] = 'Regrading attempt ({$a->done}/{$a->count}) - Attempt {$a->attemptnum} by {$a->name} (id {$a->attemptid})';
 $string['show'] = 'Show / download';
 $string['showattempts'] = 'Only show / download attempts';
diff --git a/mod/quiz/report/overview/report.php b/mod/quiz/report/overview/report.php
index b0f66d27853..e8fca33fd0e 100644
--- a/mod/quiz/report/overview/report.php
+++ b/mod/quiz/report/overview/report.php
@@ -337,8 +337,9 @@ class quiz_overview_report extends quiz_attempts_report {
      * @param bool $dryrun if true, do a pretend regrade, otherwise do it for real.
      * @param array $slots if null, regrade all questions, otherwise, just regrade
      *      the questions with those slots.
+     * @return array messages array with keys slot number, and values reasons why that slot cannot be regraded.
      */
-    public function regrade_attempt($attempt, $dryrun = false, $slots = null) {
+    public function regrade_attempt($attempt, $dryrun = false, $slots = null): array {
         global $DB;
         // Need more time for a quiz with many questions.
         core_php_time_limit::raise(300);
@@ -351,12 +352,19 @@ class quiz_overview_report extends quiz_attempts_report {
             $slots = $quba->get_slots();
         }
 
+        $messages = [];
         $finished = $attempt->state == quiz_attempt::FINISHED;
         foreach ($slots as $slot) {
             $qqr = new stdClass();
             $qqr->oldfraction = $quba->get_question_fraction($slot);
             $otherquestionversion = $this->get_new_question_for_regrade($attempt, $quba, $slot);
 
+            $message = $quba->validate_can_regrade_with_other_version($slot, $otherquestionversion);
+            if ($message) {
+                $messages[$slot] = $message;
+                continue;
+            }
+
             $quba->regrade_question($slot, $finished, null, $otherquestionversion);
 
             $qqr->newfraction = $quba->get_question_fraction($slot);
@@ -391,6 +399,7 @@ class quiz_overview_report extends quiz_attempts_report {
         $quba = null;
         $transaction = null;
         gc_collect_cycles();
+        return $messages;
     }
 
     /**
@@ -555,6 +564,7 @@ class quiz_overview_report extends quiz_attempts_report {
      */
     protected function regrade_batch_of_attempts($quiz, array $attempts,
             bool $dryrun, \core\dml\sql_join $groupstudentsjoins) {
+        global $OUTPUT;
         $this->clear_regrade_table($quiz, $groupstudentsjoins);
 
         $progressbar = new progress_bar('quiz_overview_regrade', 500, true);
@@ -572,7 +582,17 @@ class quiz_overview_report extends quiz_attempts_report {
             }
             $progressbar->update($a['done'], $a['count'],
                     get_string('regradingattemptxofywithdetails', 'quiz_overview', $a));
-            $this->regrade_attempt($attempt, $dryrun, $attempt->regradeonlyslots);
+            $messages = $this->regrade_attempt($attempt, $dryrun, $attempt->regradeonlyslots);
+            if ($messages) {
+                $items = [];
+                foreach ($messages as $slot => $message) {
+                    $items[] = get_string('regradingattemptissue', 'quiz_overview',
+                            ['slot' => $slot, 'reason' => $message]);
+                }
+                echo $OUTPUT->notification(
+                        html_writer::tag('p', get_string('regradingattemptxofyproblem', 'quiz_overview', $a)) .
+                        html_writer::alist($items), \core\output\notification::NOTIFY_WARNING);
+            }
         }
         $progressbar->update($a['done'], $a['count'],
                 get_string('regradedsuccessfullyxofy', 'quiz_overview', $a));
diff --git a/mod/quiz/report/overview/tests/behat/regrading.feature b/mod/quiz/report/overview/tests/behat/regrading.feature
index d12594b2134..d6ab3f47ffd 100644
--- a/mod/quiz/report/overview/tests/behat/regrading.feature
+++ b/mod/quiz/report/overview/tests/behat/regrading.feature
@@ -52,8 +52,8 @@ Feature: Regrading quiz attempts using the Grades report
     # Also, nothing has changed in the quiz, so the regrade won't alter any scores,
     # but this is still a useful test that the regrade process completes without errors.
     Then I should see "Quiz for testing regrading"
-    And I should see "Successfully regraded (2/2)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (2/2)"
+    And I should see "Regrade completed"
     And I press "Continue"
 
     # These next tests just serve to check we got back to the report.
@@ -67,8 +67,8 @@ Feature: Regrading quiz attempts using the Grades report
 
     And I press "Regrade selected attempts"
     Then I should see "Quiz for testing regrading"
-    And I should see "Successfully regraded (1/1)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (1/1)"
+    And I should see "Regrade completed"
     And I press "Continue"
 
     # These next tests just serve to check we got back to the report.
@@ -88,8 +88,8 @@ Feature: Regrading quiz attempts using the Grades report
 
     # Note, the order is not defined, so we can only check part of the message.
     Then I should see "Quiz for testing regrading"
-    And I should see "Successfully regraded (2/2)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (2/2)"
+    And I should see "Regrade completed"
     And I press "Continue"
 
     And "Student One" row "Regrade" column of "attempts" table should not contain "Needed"
@@ -100,8 +100,8 @@ Feature: Regrading quiz attempts using the Grades report
     And "Student TwoReview attempt" row "Grade/100.00Sort by Grade/100.00 Ascending" column of "attempts" table should contain "90.00/75.00"
     And I press "Regrade attempts marked as needing regrading (1)"
     And I should see "Quiz for testing regrading"
-    And I should see "Successfully regraded (1/1)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (1/1)"
+    And I should see "Regrade completed"
     And I press "Continue"
 
     # These next tests just serve to check we got back to the report.
@@ -117,8 +117,8 @@ Feature: Regrading quiz attempts using the Grades report
     And I navigate to "Results" in current page administration
     When I press "Dry run a full regrade"
     Then I should see "Quiz for testing regrading"
-    And I should see "Successfully regraded (2/2)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (2/2)"
+    And I should see "Regrade completed"
     And I press "Continue"
     And I should see "Quiz for testing regrading"
     And I should see "Overall number of students achieving grade ranges"
@@ -132,12 +132,12 @@ Feature: Regrading quiz attempts using the Grades report
     And I click on "v2 (latest)" "option"
     And I navigate to "Results" in current page administration
     And I press "Dry run a full regrade"
-    And I should see "Regrade completed successfully"
+    And I should see "Regrade completed"
     And I press "Continue"
     And "student1@example.com" row "Regrade" column of "attempts" table should contain "Needed"
     And "Correct" "icon" should appear before "50.00/0.00" "text"
     And I press "Regrade all"
-    And I should see "Regrade completed successfully"
+    And I should see "Regrade completed"
     And I press "Continue"
     Then "student1@example.com" row "Regrade" column of "attempts" table should contain "Done"
     And "Student OneReview attempt" row "Q. 1/50.00Sort by Q. 1/50.00 Ascending" column of "attempts" table should contain "50.00/0.00"
@@ -177,8 +177,8 @@ Feature: Regrading quiz attempts using the Grades report
     And I click on "Always latest" "option"
     And I navigate to "Results" in current page administration
     And I press "Regrade all"
-    And I should see "Successfully regraded (1/1)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (1/1)"
+    And I should see "Regrade completed"
     And I press "Continue"
     Then "student3@example.com" row "Q. 1/50.00Sort by Q. 1/50.00 Ascending" column of "attempts" table should contain "50.00/0.00"
     And "Incorrect" "icon" should appear before "50.00/0.00" "text"
@@ -218,8 +218,8 @@ Feature: Regrading quiz attempts using the Grades report
     And "student3@example.com" row "Q. 1/100.00Sort by Q. 1/100.00 Ascending" column of "attempts" table should contain "100.00"
     And "Correct" "icon" should be visible
     And I press "Regrade all"
-    And I should see "Successfully regraded (1/1)"
-    And I should see "Regrade completed successfully"
+    And I should see "Finished regrading (1/1)"
+    And I should see "Regrade completed"
     And I press "Continue"
     Then "student3@example.com" row "Q. 1/100.00Sort by Q. 1/100.00 Ascending" column of "attempts" table should contain "100.00/0.00"
     And "Incorrect" "icon" should be visible
diff --git a/mod/quiz/upgrade.txt b/mod/quiz/upgrade.txt
index 2419d36bf44..17a73e8d847 100644
--- a/mod/quiz/upgrade.txt
+++ b/mod/quiz/upgrade.txt
@@ -1,5 +1,13 @@
 This files describes API changes in the quiz code.
 
+=== 4.0.2, 4.1 ===
+
+* No external code should be calling quiz_overview_report::regrade_attempt because it is an
+  internal method of the quiz_overview plugin. But if you are incorrectly using it, be aware
+  that the API changed slightly. It now returns an array listing any questions which could
+  not be regraded.
+
+
 === 4.0 ===
 
 * The following API methods have a new parameter, $studentisonline, to define whether the student is currently interacting:
diff --git a/question/engine/questionattempt.php b/question/engine/questionattempt.php
index ba41f67118a..097465c7a42 100644
--- a/question/engine/questionattempt.php
+++ b/question/engine/questionattempt.php
@@ -1396,6 +1396,16 @@ class question_attempt {
         $this->process_action(array('-finish' => 1), $timestamp, $userid);
     }
 
+    /**
+     * Verify if this question_attempt in can be regraded with that other question version.
+     *
+     * @param question_definition $otherversion a different version of the question to use in the regrade.
+     * @return string|null null if the regrade can proceed, else a reason why not.
+     */
+    public function validate_can_regrade_with_other_version(question_definition $otherversion): ?string {
+        return $this->get_question(false)->validate_can_regrade_with_other_version($otherversion);
+    }
+
     /**
      * Perform a regrade. This replays all the actions from $oldqa into this
      * attempt.
@@ -1412,7 +1422,8 @@ class question_attempt {
             if ($first) {
                 // First step of the attempt.
                 $first = false;
-                $this->start($oldqa->behaviour, $oldqa->get_variant(), $step->get_all_data(),
+                $this->start($oldqa->behaviour, $oldqa->get_variant(),
+                        $this->get_attempt_state_data_to_regrade_with_version($step, $oldqa->get_question()),
                         $step->get_timecreated(), $step->get_user_id(), $step->get_id());
 
             } else if ($step->has_behaviour_var('finish') && count($step->get_submitted_data()) > 1) {
@@ -1446,6 +1457,27 @@ class question_attempt {
         $this->set_flagged($oldqa->is_flagged());
     }
 
+    /**
+     * Helper used by regrading.
+     *
+     * Get the data from the first step of the old attempt and, if necessary,
+     * update it to be suitable for use with the other version of the question.
+     *
+     * @param question_attempt_step $oldstep First step at an attempt at $otherversion of this question.
+     * @param question_definition $otherversion Another version of the question being attempted.
+     * @return array updated data required to restart an attempt with the current version of this question.
+     */
+    protected function get_attempt_state_data_to_regrade_with_version(question_attempt_step $oldstep,
+            question_definition $otherversion): array {
+        if ($this->get_question(false) === $otherversion) {
+            return $oldstep->get_all_data();
+        } else {
+            $attemptstatedata = $this->get_question(false)->update_attempt_state_data_for_new_version(
+                    $oldstep, $otherversion);
+            return array_merge($attemptstatedata, $oldstep->get_behaviour_data());
+        }
+    }
+
     /**
      * Change the max mark for this question_attempt.
      * @param float $maxmark the new max mark.
diff --git a/question/engine/questionusage.php b/question/engine/questionusage.php
index 291285684f5..116eca571de 100644
--- a/question/engine/questionusage.php
+++ b/question/engine/questionusage.php
@@ -875,9 +875,21 @@ class question_usage_by_activity {
         $this->observer->notify_attempt_modified($qa);
     }
 
+    /**
+     * Verify if the question_attempt in the given slot can be regraded with that other question version.
+     *
+     * @param int $slot the number used to identify this question within this usage.
+     * @param question_definition $otherversion a different version of the question to use in the regrade.
+     * @return string|null null if the regrade can proceed, else a reason why not.
+     */
+    public function validate_can_regrade_with_other_version(int $slot, question_definition $otherversion): ?string {
+        return $this->get_question_attempt($slot)->validate_can_regrade_with_other_version($otherversion);
+    }
+
     /**
      * Regrade a question in this usage. This replays the sequence of submitted
      * actions to recompute the outcomes.
+     *
      * @param int $slot the number used to identify this question within this usage.
      * @param bool $finished whether the question attempt should be forced to be finished
      *      after the regrade, or whether it may still be in progress (default false).
diff --git a/question/type/questionbase.php b/question/type/questionbase.php
index e7d63600571..874b109406b 100644
--- a/question/type/questionbase.php
+++ b/question/type/questionbase.php
@@ -211,6 +211,53 @@ abstract class question_definition {
     public function apply_attempt_state(question_attempt_step $step) {
     }
 
+    /**
+     * Verify if an attempt at this question can be re-graded using the other question version.
+     *
+     * To put it another way, will {@see update_attempt_state_date_from_old_version()} be able to work?
+     *
+     * It is expected that this relationship is symmetrical, so if you can regrade from V1 to V3, then
+     * you can change back from V3 to V1.
+     *
+     * @param question_definition $otherversion a different version of the question to use in the regrade.
+     * @return string|null null if the regrade can proceed, else a reason why not.
+     */
+    public function validate_can_regrade_with_other_version(question_definition $otherversion): ?string {
+        if (get_class($otherversion) !== get_class($this)) {
+            return get_string('cannotregradedifferentqtype', 'question');
+        }
+
+        return null;
+    }
+
+    /**
+     * Update the data representing the initial state of an attempt another version of this question, to allow for the changes.
+     *
+     * What is required is probably most easily understood using an example. Think about multiple choice questions.
+     * The first step has a variable '_order' which is a comma-separated list of question_answer ids.
+     * A different version of the question will have different question_answers with different ids. However, the list of
+     * choices should be similar, and so we need to shuffle the new list of ids in the same way that the old one was.
+     *
+     * This method should only be called if {@see validate_can_regrade_with_other_version()} did not
+     * flag up a potential problem. So, this method will throw a {@see coding_exception} if it is not
+     * possible to work out a return value.
+     *
+     * @param question_attempt_step $oldstep the first step of a {@see question_attempt} at $oldquestion.
+     * @param question_definition $oldquestion the previous version of the question, which $oldstate comes from.
+     * @return array the submit data which can be passed to {@see apply_attempt_state} to start
+     *     an attempt at this version of this question, corresponding to the attempt at the old question.
+     * @throws coding_exception if this can't be done.
+     */
+    public function update_attempt_state_data_for_new_version(
+            question_attempt_step $oldstep, question_definition $oldquestion) {
+        $message = $this->validate_can_regrade_with_other_version($oldquestion);
+        if ($message) {
+            throw new coding_exception($message);
+        }
+
+        return $oldstep->get_qt_data();
+    }
+
     /**
      * Generate a brief, plain-text, summary of this question. This is used by
      * various reports. This should show the particular variant of the question
diff --git a/question/type/upgrade.txt b/question/type/upgrade.txt
index 87f56205535..10d1a0c3ddc 100644
--- a/question/type/upgrade.txt
+++ b/question/type/upgrade.txt
@@ -1,17 +1,32 @@
 This files describes API changes for question type plugins.
 
+=== 4.0.2, 4.1 ===
+
+* There was one issue caused by the changes in Moodle 4.0 which requires changes in question types,
+  and that is regrading. There are two new methods which some question types will need to implement,
+   - validate_can_regrade_with_other_version
+   - update_attempt_state_data_for_new_version
+  these methods are introduced in this commit, and there are details PHPdoc comments about what they
+  must do. Then the immediately following commits implement them in the core question types where
+  they are required.
+  Generally, you will need to implement one or both of these if you question type does something
+  significant in the apply_attempt_state method. If you have not implemented that method, then
+  almost certainly you don't need to worry about this.
+
+
 === 4.0 ===
 
-1) The major question bank changes should not affect most basic question type plugins.
-   The navigation changes may affect Behat tests. If you encounter this,
-   the best way to fix it is to use the new navigation steps in MDL-74130.
+* The major question bank changes should not affect most basic question type plugins.
+  The navigation changes may affect Behat tests. If you encounter this,
+  the best way to fix it is to use the new navigation steps in MDL-74130.
 
-2) The qualification 'most' is because some question types do more complex things, which
-   will require changes related to question versionning. Some examples that come to mind:
+* The qualification 'most' is because some question types do more complex things, which
+  will require changes related to question versionning. Some examples that come to mind:
    - the way qtype_mulitanswer (or qtype_combined) aggregates several sub-questions into a parent question.
    - the way some contrib plugins (e.g. qtype_stack, qtype_pmatch) store additional data (question tests)
      linked to questions. That relationship will need to be updated.
 
+
 === 3.11 ===
 
 * Introducing the following \question_type base class methods to save/fetch the last form values
@@ -42,6 +57,7 @@ This files describes API changes for question type plugins.
   use it in a question type at
   https://github.com/moodleou/moodle-qtype_pmatch/commit/2aefa8b5dcc7bab768f4707a4ffb7befcf4c2540.
 
+
 === 3.8, 3.7.3, 3.6.7 ===
 
 * Coming up in Moodle 3.8 are some changes to the question bank UI. These will break any