It's no wonder that peonies (Paeonia spp.) appear in paintings, flower arrangements and other works of art, as their ruffled, colorful blooms easily capture your attention. Depending on the specific variety, peonies grow in U.S. Department of Agriculture plant hardiness zones 3 through 8. Peonies need a nutrient-rich, moist soil with a neutral pH and full sun. Buds begin to appear in spring and open in late spring to early summer. Removing the smaller side buds, known as disbudding, as soon as they appear, will encourage larger terminal blooms. Deadheading faded blooms will keep the plant looking neat and divert its energy into storing strength for next year’s flowers.