The full review history is only available to users with the moderator tools privilege (10k+ users on designed sites).
If you don't have enough rep to see the full review history, though, you still have enough information to deduce the last few recent reviews.
On the review homepage (
/review), all users can see the last six users who reviewed tasks in each queue, as well as the amount of time since they last reviewed a task. Clicking on any avatar will direct you to that user's profile, after which you can use Shadow's method in the other answer to see reviews cast by that user.
Note that reviews in the Low Quality Posts review queue aren't in the public list; this is to prevent onlookers from getting an incorrect perspective of one's review history (since reviews on deleted posts aren't shown there).