If you've recently planted peonies or have young plants, it's possible that they're simply not mature enough to bloom yet. Peony bushes may take up to 3 years to bloom. Be patient.
Peonies need at least six hours of sun a day. If they are planted in a shady spot they may not be receive enough sunlight to produce blooms. Consider moving them to a sunnier location.
Plant bare root peonies no deeper than 2" below the soil line. Potted peonies can be planted with the soil of the pot even with the ground's soil line. If initially planted too deep, when the plant is dormant in the fall you can raise it up a bit.
In conclusion, if your peonies aren't blooming, there are several possible reasons why.
By addressing these common issues, you can help ensure that your peonies produce the beautiful, fragrant blooms you've been waiting for.