diff --git a/backend/app/Http/Controllers/ScheduleController.php b/backend/app/Http/Controllers/ScheduleController.php
index 9ec6588..f80461a 100644
--- a/backend/app/Http/Controllers/ScheduleController.php
+++ b/backend/app/Http/Controllers/ScheduleController.php
@@ -14,6 +14,8 @@ use App\Schedule\UseCases\GetSchedule\GetScheduleRequest;
 use App\Schedule\UseCases\ListSchedules\ListSchedules;
 use App\Schedule\UseCases\ListAssignmentsForDate\ListAssignmentsForDate;
 use App\Schedule\UseCases\ListAssignmentsForDate\ListAssignmentsForDateRequest;
+use App\Schedule\UseCases\SetAssignmentCompletion\SetAssignmentCompletion;
+use App\Schedule\UseCases\SetAssignmentCompletion\SetAssignmentCompletionRequest;
 use App\Shared\Http\RequestInput;
 use App\User\User;
 use Illuminate\Http\JsonResponse;
@@ -26,6 +28,7 @@ class ScheduleController extends Controller
         private ListSchedules $listSchedules,
         private GetSchedule $getSchedule,
         private ListAssignmentsForDate $listAssignmentsForDate,
+        private SetAssignmentCompletion $setAssignmentCompletion,
     ) {}
 
     public function store(Request $request): JsonResponse
@@ -124,6 +127,41 @@ class ScheduleController extends Controller
         ]);
     }
 
+    public function updateAssignment(
+        Request $request,
+        int $assignmentId,
+    ): JsonResponse {
+        $input = new RequestInput($request);
+
+        try {
+            $assignment = $this->setAssignmentCompletion->execute(
+                new SetAssignmentCompletionRequest(
+                    assignmentId: $assignmentId,
+                    user: $this->user($request),
+                    completed: $input->boolean('completed'),
+                ),
+            );
+        } catch (BadRequestException $exception) {
+            return new JsonResponse(
+                ['error' => $exception->getMessage()],
+                400,
+            );
+        } catch (NotFoundException $exception) {
+            return new JsonResponse(
+                ['error' => $exception->getMessage()],
+                404,
+            );
+        }
+
+        return new JsonResponse([
+            'assignment' => [
+                'id' => $assignment->getId(),
+                'completedAt' => $assignment->getCompletedAt()
+                    ?->format(DATE_ATOM),
+            ],
+        ]);
+    }
+
     /**
      * @return array<string, mixed>
      */
@@ -180,7 +218,7 @@ class ScheduleController extends Controller
     }
 
     /**
-     * @return array{id: int, element: array{
+     * @return array{id: int, completedAt: string|null, element: array{
      *     name: string,
      *     kind: string,
      *     path: list<string>
@@ -191,6 +229,8 @@ class ScheduleController extends Controller
     ): array {
         return [
             'id' => $assignment->getId(),
+            'completedAt' => $assignment->getCompletedAt()
+                ?->format(DATE_ATOM),
             'element' => [
                 'name' => $assignment->getName(),
                 'kind' => $assignment->getKind(),
diff --git a/backend/app/Schedule/EloquentScheduleRepository.php b/backend/app/Schedule/EloquentScheduleRepository.php
index 7aec036..8cbde2a 100644
--- a/backend/app/Schedule/EloquentScheduleRepository.php
+++ b/backend/app/Schedule/EloquentScheduleRepository.php
@@ -5,6 +5,7 @@ namespace App\Schedule;
 use App\User\User;
 use DateTimeImmutable;
 use DateTimeZone;
+use DomainException;
 use Illuminate\Support\Facades\DB;
 
 class EloquentScheduleRepository implements ScheduleRepository
@@ -29,6 +30,7 @@ class EloquentScheduleRepository implements ScheduleRepository
                     'scheduled_date' => $assignmentDto->scheduledDate
                         ->format('Y-m-d'),
                     'position' => $assignmentDto->position,
+                    'completed_at' => null,
                 ]);
             }
 
@@ -77,6 +79,7 @@ class EloquentScheduleRepository implements ScheduleRepository
             ->where('schedule_assignments.scheduled_date', $date->format(
                 'Y-m-d',
             ))
+            ->whereNull('schedule_assignments.completed_at')
             ->with('schedule')
             ->orderByDesc('schedules.id')
             ->orderBy('schedule_assignments.position')
@@ -95,6 +98,50 @@ class EloquentScheduleRepository implements ScheduleRepository
         return $assignments;
     }
 
+    public function findAssignmentForUser(
+        int $id,
+        User $user,
+    ): ?ScheduleAssignment {
+        $model = ScheduleAssignmentModel::query()
+            ->select('schedule_assignments.*')
+            ->join(
+                'schedules',
+                'schedules.id',
+                '=',
+                'schedule_assignments.schedule_id',
+            )
+            ->where('schedule_assignments.id', $id)
+            ->where('schedules.user_id', $user->getId())
+            ->first();
+
+        return $model === null
+            ? null
+            : $this->assignmentToDomain($model);
+    }
+
+    public function updateAssignment(
+        ScheduleAssignment $assignment,
+    ): ScheduleAssignment {
+        $query = ScheduleAssignmentModel::query()
+            ->whereKey($assignment->getId());
+        if ($assignment->getCompletedAt() === null) {
+            $query->update(['completed_at' => null]);
+        } else {
+            $query->whereNull('completed_at')->update([
+                'completed_at' => $assignment->getCompletedAt(),
+            ]);
+        }
+
+        $model = ScheduleAssignmentModel::find($assignment->getId());
+        if ($model === null) {
+            throw new DomainException(
+                "Assignment with id {$assignment->getId()} not found",
+            );
+        }
+
+        return $this->assignmentToDomain($model);
+    }
+
     private function toDomain(ScheduleModel $model, User $user): Schedule
     {
         $assignmentModels = ScheduleAssignmentModel::query()
@@ -129,6 +176,9 @@ class EloquentScheduleRepository implements ScheduleRepository
             path: $model->element_path,
             scheduledDate: $this->date($model->scheduled_date),
             position: $model->position,
+            completedAt: $model->completed_at === null
+                ? null
+                : $this->dateTime($model->completed_at),
         );
     }
 
@@ -136,4 +186,10 @@ class EloquentScheduleRepository implements ScheduleRepository
     {
         return new DateTimeImmutable($value, new DateTimeZone('UTC'));
     }
+
+    private function dateTime(DateTimeImmutable $value): DateTimeImmutable
+    {
+        return DateTimeImmutable::createFromInterface($value)
+            ->setTimezone(new DateTimeZone('UTC'));
+    }
 }
diff --git a/backend/app/Schedule/ScheduleAssignment.php b/backend/app/Schedule/ScheduleAssignment.php
index 482b45d..8f90435 100644
--- a/backend/app/Schedule/ScheduleAssignment.php
+++ b/backend/app/Schedule/ScheduleAssignment.php
@@ -4,7 +4,7 @@ namespace App\Schedule;
 
 use DateTimeImmutable;
 
-final readonly class ScheduleAssignment
+final class ScheduleAssignment
 {
     /**
      * @param list<string> $path
@@ -16,6 +16,7 @@ final readonly class ScheduleAssignment
         private array $path,
         private DateTimeImmutable $scheduledDate,
         private int $position,
+        private ?DateTimeImmutable $completedAt,
     ) {}
 
     public function getId(): int
@@ -50,4 +51,21 @@ final readonly class ScheduleAssignment
     {
         return $this->position;
     }
+
+    public function getCompletedAt(): ?DateTimeImmutable
+    {
+        return $this->completedAt;
+    }
+
+    public function complete(DateTimeImmutable $completedAt): void
+    {
+        if ($this->completedAt === null) {
+            $this->completedAt = $completedAt;
+        }
+    }
+
+    public function reopen(): void
+    {
+        $this->completedAt = null;
+    }
 }
diff --git a/backend/app/Schedule/ScheduleAssignmentModel.php b/backend/app/Schedule/ScheduleAssignmentModel.php
index 3cd5577..33b2953 100644
--- a/backend/app/Schedule/ScheduleAssignmentModel.php
+++ b/backend/app/Schedule/ScheduleAssignmentModel.php
@@ -2,6 +2,7 @@
 
 namespace App\Schedule;
 
+use DateTimeImmutable;
 use Illuminate\Database\Eloquent\Attributes\Fillable;
 use Illuminate\Database\Eloquent\Builder;
 use Illuminate\Database\Eloquent\Model;
@@ -15,6 +16,7 @@ use Illuminate\Database\Eloquent\Relations\BelongsTo;
  * @property list<string> $element_path
  * @property string $scheduled_date
  * @property int $position
+ * @property DateTimeImmutable|null $completed_at
  * @property-read ScheduleModel $schedule
  *
  * @method static Builder<static>|ScheduleAssignmentModel newModelQuery()
@@ -30,6 +32,7 @@ use Illuminate\Database\Eloquent\Relations\BelongsTo;
     'element_path',
     'scheduled_date',
     'position',
+    'completed_at',
 ])]
 class ScheduleAssignmentModel extends Model
 {
@@ -46,6 +49,7 @@ class ScheduleAssignmentModel extends Model
             'schedule_id' => 'integer',
             'element_path' => 'array',
             'position' => 'integer',
+            'completed_at' => 'immutable_datetime',
         ];
     }
 
diff --git a/backend/app/Schedule/ScheduleRepository.php b/backend/app/Schedule/ScheduleRepository.php
index fcdcb8c..3222311 100644
--- a/backend/app/Schedule/ScheduleRepository.php
+++ b/backend/app/Schedule/ScheduleRepository.php
@@ -23,4 +23,13 @@ interface ScheduleRepository
         User $user,
         DateTimeImmutable $date,
     ): array;
+
+    public function findAssignmentForUser(
+        int $id,
+        User $user,
+    ): ?ScheduleAssignment;
+
+    public function updateAssignment(
+        ScheduleAssignment $assignment,
+    ): ScheduleAssignment;
 }
diff --git a/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletion.php b/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletion.php
new file mode 100644
index 0000000..df66b8d
--- /dev/null
+++ b/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletion.php
@@ -0,0 +1,47 @@
+<?php
+
+namespace App\Schedule\UseCases\SetAssignmentCompletion;
+
+use App\Auth\Clock;
+use App\Exceptions\BadRequestException;
+use App\Exceptions\NotFoundException;
+use App\Schedule\ScheduleAssignment;
+use App\Schedule\ScheduleRepository;
+
+class SetAssignmentCompletion
+{
+    public function __construct(
+        private ScheduleRepository $scheduleRepository,
+        private Clock $clock,
+    ) {}
+
+    /**
+     * @throws BadRequestException
+     * @throws NotFoundException
+     */
+    public function execute(
+        SetAssignmentCompletionRequest $request,
+    ): ScheduleAssignment {
+        if ($request->completed === null) {
+            throw new BadRequestException(
+                'completed must be a boolean',
+            );
+        }
+
+        $assignment = $this->scheduleRepository->findAssignmentForUser(
+            $request->assignmentId,
+            $request->user,
+        );
+        if ($assignment === null) {
+            throw new NotFoundException('assignment not found');
+        }
+
+        if ($request->completed) {
+            $assignment->complete($this->clock->now());
+        } else {
+            $assignment->reopen();
+        }
+
+        return $this->scheduleRepository->updateAssignment($assignment);
+    }
+}
diff --git a/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletionRequest.php b/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletionRequest.php
new file mode 100644
index 0000000..e591375
--- /dev/null
+++ b/backend/app/Schedule/UseCases/SetAssignmentCompletion/SetAssignmentCompletionRequest.php
@@ -0,0 +1,14 @@
+<?php
+
+namespace App\Schedule\UseCases\SetAssignmentCompletion;
+
+use App\User\User;
+
+final readonly class SetAssignmentCompletionRequest
+{
+    public function __construct(
+        public int $assignmentId,
+        public User $user,
+        public ?bool $completed,
+    ) {}
+}
diff --git a/backend/app/Shared/Http/RequestInput.php b/backend/app/Shared/Http/RequestInput.php
index 322817a..3ea93dc 100644
--- a/backend/app/Shared/Http/RequestInput.php
+++ b/backend/app/Shared/Http/RequestInput.php
@@ -27,4 +27,11 @@ class RequestInput
 
         return is_int($value) ? $value : null;
     }
+
+    public function boolean(string $key): ?bool
+    {
+        $value = $this->request->input($key);
+
+        return is_bool($value) ? $value : null;
+    }
 }
diff --git a/backend/database/migrations/2026_08_10_000001_create_schedule_assignments_table.php b/backend/database/migrations/2026_08_10_000001_create_schedule_assignments_table.php
index b52c60a..c98992a 100644
--- a/backend/database/migrations/2026_08_10_000001_create_schedule_assignments_table.php
+++ b/backend/database/migrations/2026_08_10_000001_create_schedule_assignments_table.php
@@ -20,10 +20,12 @@ return new class extends Migration
                 $table->json('element_path');
                 $table->date('scheduled_date');
                 $table->unsignedInteger('position');
+                $table->timestamp('completed_at')->nullable();
                 $table->unique(['schedule_id', 'position']);
                 $table->index([
                     'schedule_id',
                     'scheduled_date',
+                    'completed_at',
                     'position',
                 ]);
             },
diff --git a/backend/routes/api.php b/backend/routes/api.php
index 2355570..76caf16 100644
--- a/backend/routes/api.php
+++ b/backend/routes/api.php
@@ -16,6 +16,10 @@ Route::middleware(AuthMiddleware::class)->group(function (): void {
     Route::get('/sets/{setId}', [SetController::class, 'show'])
         ->whereNumber('setId');
     Route::get('/assignments', [ScheduleController::class, 'assignments']);
+    Route::patch(
+        '/assignments/{assignmentId}',
+        [ScheduleController::class, 'updateAssignment'],
+    )->whereNumber('assignmentId');
     Route::post('/schedules', [ScheduleController::class, 'store']);
     Route::get('/schedules', [ScheduleController::class, 'index']);
     Route::get('/schedules/{scheduleId}', [ScheduleController::class, 'show'])
diff --git a/backend/tests/Fakes/FakeScheduleRepository.php b/backend/tests/Fakes/FakeScheduleRepository.php
index e30caf2..e2f35bc 100644
--- a/backend/tests/Fakes/FakeScheduleRepository.php
+++ b/backend/tests/Fakes/FakeScheduleRepository.php
@@ -9,6 +9,7 @@ use App\Schedule\ScheduleAssignment;
 use App\Schedule\ScheduleRepository;
 use App\User\User;
 use DateTimeImmutable;
+use DomainException;
 
 class FakeScheduleRepository implements ScheduleRepository
 {
@@ -17,6 +18,8 @@ class FakeScheduleRepository implements ScheduleRepository
      */
     private array $schedules = [];
 
+    private int $nextAssignmentId = 1;
+
     public function create(CreateScheduleDto $dto): Schedule
     {
         $id = count($this->schedules) + 1;
@@ -24,12 +27,13 @@ class FakeScheduleRepository implements ScheduleRepository
 
         foreach ($dto->assignments as $assignmentDto) {
             $assignments[] = new ScheduleAssignment(
-                id: count($assignments) + 1,
+                id: $this->nextAssignmentId++,
                 name: $assignmentDto->name,
                 kind: $assignmentDto->kind,
                 path: $assignmentDto->path,
                 scheduledDate: $assignmentDto->scheduledDate,
                 position: $assignmentDto->position,
+                completedAt: null,
             );
         }
 
@@ -84,6 +88,7 @@ class FakeScheduleRepository implements ScheduleRepository
             foreach ($schedule->getAssignments() as $assignment) {
                 if ($assignment->getScheduledDate()->format('Y-m-d')
                     !== $date->format('Y-m-d')
+                    || $assignment->getCompletedAt() !== null
                 ) {
                     continue;
                 }
@@ -99,21 +104,66 @@ class FakeScheduleRepository implements ScheduleRepository
         return $assignments;
     }
 
+    public function findAssignmentForUser(
+        int $id,
+        User $user,
+    ): ?ScheduleAssignment {
+        foreach ($this->findAllForUser($user) as $schedule) {
+            foreach ($schedule->getAssignments() as $assignment) {
+                if ($assignment->getId() === $id) {
+                    return $this->copyAssignment($assignment);
+                }
+            }
+        }
+
+        return null;
+    }
+
+    public function updateAssignment(
+        ScheduleAssignment $assignment,
+    ): ScheduleAssignment {
+        foreach ($this->schedules as $id => $schedule) {
+            $assignments = [];
+            $found = false;
+
+            foreach ($schedule->getAssignments() as $storedAssignment) {
+                if ($storedAssignment->getId() === $assignment->getId()) {
+                    $assignments[] = $this->copyAssignment($assignment);
+                    $found = true;
+                } else {
+                    $assignments[] = $this->copyAssignment(
+                        $storedAssignment,
+                    );
+                }
+            }
+
+            if ($found) {
+                $this->schedules[$id] = new Schedule(
+                    id: $schedule->getId(),
+                    user: $schedule->getUser(),
+                    setName: $schedule->getSetName(),
+                    elementKind: $schedule->getElementKind(),
+                    startDate: $schedule->getStartDate(),
+                    targetDate: $schedule->getTargetDate(),
+                    assignments: $assignments,
+                );
+
+                return $this->copyAssignment($assignment);
+            }
+        }
+
+        throw new DomainException(
+            "Assignment with id {$assignment->getId()} not found",
+        );
+    }
+
     private function copy(Schedule $schedule): Schedule
     {
-        $assignments = array_map(
-            function (ScheduleAssignment $assignment): ScheduleAssignment {
-                return new ScheduleAssignment(
-                    id: $assignment->getId(),
-                    name: $assignment->getName(),
-                    kind: $assignment->getKind(),
-                    path: $assignment->getPath(),
-                    scheduledDate: $assignment->getScheduledDate(),
-                    position: $assignment->getPosition(),
-                );
-            },
-            $schedule->getAssignments(),
-        );
+        $assignments = array_map(function (
+            ScheduleAssignment $assignment,
+        ): ScheduleAssignment {
+            return $this->copyAssignment($assignment);
+        }, $schedule->getAssignments());
 
         return new Schedule(
             id: $schedule->getId(),
@@ -125,4 +175,18 @@ class FakeScheduleRepository implements ScheduleRepository
             assignments: $assignments,
         );
     }
+
+    private function copyAssignment(
+        ScheduleAssignment $assignment,
+    ): ScheduleAssignment {
+        return new ScheduleAssignment(
+            id: $assignment->getId(),
+            name: $assignment->getName(),
+            kind: $assignment->getKind(),
+            path: $assignment->getPath(),
+            scheduledDate: $assignment->getScheduledDate(),
+            position: $assignment->getPosition(),
+            completedAt: $assignment->getCompletedAt(),
+        );
+    }
 }