To access a record of all changes made on a board, please go to Tools - Changelog.
The Changelog is the place to go to find what kinds of changes have been applied to the board, and by whom. This information can be displayed for chosen time-frames, limited by people making the changes and by the type of change.
You can be viewing all recorded changes, just the task moves, additions of comments only, or task changes alone.
Great if you need to know who suddenly shortened the due dates for all your tasks ;)