Peony’s have to be my favorite flower. Huge blossoms, wide variety of styles – double, fancy, they have an antique look to them that looks great in still life photographs. The plants themselves look great as foliage and especially as a small hedge row. They can be divided but they don’t like to be moved around, often they can take up to two years to bloom after being moved.
The peony is named after Paeon (also spelled Paean), a student of Asclepius, the Greek god of medicine and healing. Asclepius became jealous of his pupil; Zeus saved Paeon from the wrath of Asclepius by turning him into the peony flower.
Herbaceous and Itoh peonies are propagated by root division, and sometimes by seed. Tree peonies can be propagated by grafting, division, seed, and from cuttings, although root grafting is most common commercially. 
Herbaceous peonies such as Paeonia lactiflora, will die back to ground level each autumn. Their stems will reappear the following spring. However tree peonies, such as Paeonia suffruticosa, are shrubbier. They produce permanent woody stems that will lose their leaves in winter but the stem itself remains intact above ground level. How you plant your peony will depend on which type you have.