We provide an introduction to the recent developments of dynamic mechanism design, with a primary focus on the quasilinear case. First, we describe socially optimal (or efficient) dynamic mechanisms. These mechanisms extend the well-known Vickrey-Clark-Groves and D'Aspremont-Gerard-Varet mechanisms to a dynamic environment. Second, we discuss revenue optimal mechanisms. We cover models of sequential screening and revenue-maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agents' types. Third, we consider models with changing populations of agents over time. After discussing related models with risk-averse agents and limited liability, we conclude with a number of open questions and challenges that remain for the theory of dynamic mechanism design.