Abstract: Three topics are discussed. The first is a research program to establish whether the familiar trading rules, such as sealed-bid and oral double auctions, are incentive efficient over a wide class of economic environments. The second is a review of recent studies of dynamic trading processes, and particularly the effects of impatience and private information on the timing and terms of trade; the main emphasis is on models of bilateral bargaining. The third considers prospects for embedding bargaining and auction models in larger environments so as to endogenize traders' impatience as a consequence of competitive pressures; models of dispersed matching and bargaining and a model of oral bid-ask markets are mentioned.