Ruffled big blooms in luscious pink, snow white, coral, red and yellow make the peony a favorite cutting flower. Like most flowering perennials, peonies require winter dormancy. Roots are best planted in full sun in early fall, with blooms arriving on established plants in late spring and early summer. Plants will last for decades with little care. Flower types, determined by petal makeup, include single, double, full double, bomb and anemone.