This paper reviews a framework for numerically analyzing dynamic interactions in imperfectly competitive industries. The framework dates back to Ericson and Pakes [1995. Review of Economic Studies 62, 53–82], but it is based on equilibrium notions that had been available for some time before, and it has been extended in many ways by different authors since. The framework requires as input a set of primitives which describe the institutional structure in the industry to be analyzed. The framework outputs profits and policies for every incumbent and potential entrant at each possible state of the industry. These policies can be used to simulate the distribution of sample paths for all firms from any initial industry structure. The sample paths generated by the model can be quite different depending on the primitives, and most of the extensions were designed to enable the framework to accommodate empirically relevant cases that required modification of the initial structure. The sample paths possess similar properties to those observed in (the recently available) panel data sets on industries. These sample paths can be used either for an analysis of the likely response to a policy or an environmental change, or as the model's implication in an estimation algorithm. We begin with a review of an elementary version of the framework and a report on what is known about its analytic properties. Much of the rest of the paper deals with computational issues. We start with an introduction to iterative techniques for computing equilibrium that are analogous to the techniques used to compute the solution to single agent dynamic programming problems. This includes discussions of the determinants of the computational burden of these techniques, and the mechanism implicitly used to select an equilibrium when multiple equilibria are possible. We then outline a number of techniques that might be used to reduce the computational burden of the iterative algorithm. This section includes discussions of both the implications of differences in modeling assumptions used in the alternative techniques, and a discussion of the likely relevance of the different techniques for different institutional structures. A separate section reports on a technique for computing multiple equilibria from the same set of primitives. The paper concludes with a review of applications of the framework and a brief discussion of areas where further development of the framework would seem warranted.