Most peonies want full sun for best flowering. The foliage does not die back. In fact, peony foliage is among the most beautiful of any perennials. Just cut off the dead flowers and enjoy. In the fall, cut off the foliage and put in the trash, not the compost, to avoid any plant diseases.

What diseases from the peonies would survive in compost? This is my first year with peonies and they were beautiful! I wish they bloomed longer though.

fungi and mold If you have a moist year the spores will be more active. Certain types such as crown rot will kill your peony. Some types you can just cut off the effected leaves and throw away.

This is the first year in about 10 that it has been wet enough in my area to be concerned.

Botrytis blight. Check it out.