Experts and BHG readers answer.
Peonies will not bloom
Thanks for writing. There are several pretty common reasons why peonies don't bloom. They include: the roots being buried too deeply in the soil (the crown, or where the shoots grow out of the leaves, should be about an inch or so under the ground); the plants not getting enough light (they bloom best with at least 6 hours of direct sun a day); and if they've been transplanted it can take a couple of years to become reestablished before they bloom again.
---Justin, Senior Garden Editor, BHG.com