You can verify if students completed an assigned peer review. In the peer review page, you can view all peer reviews left on a student's submission. You can also view a single review left by a student for an assigned peer review. Peer review comments also display in SpeedGrader along with any other comments left on the assignment.

Students don't automatically receive a grade for completing a peer review. If you want to award points for peer reviews, you can create a no submission assignment in the gradebook and assign points manually.