Dynamic contracting plays a central role in many environments—for instance, in the sale of goods and services to consumers whose preferences evolve through learning, experimentation, or habit formation; in the taxation of workers whose productivity changes with learning-by-doing; in the provision of services on platforms with stochastic entry and exit of buyers and sellers; and in the matching of agents whose values and attractiveness are gradually revealed through past interactions. This article surveys several strands of the recent dynamic mechanism design literature, distills a few lessons, and points to promising directions for future research.