Empirical models of demand for - and, often, supply of - differentiated products are widely used in practice, typically employing parametric functional forms and distributions of consumer heterogeneity. We re view some recent work studying identification in a broad class of such models. This work shows that parametric functional forms and distributional assumptions are not essential for identification. Rather, identification relies primarily on the standard requirement that instruments be available for the endogenous variables - here, typically, prices and quantities. We discuss the kinds of instruments needed for identification and how the reliance on instruments can be reduced by nonparametric functional form restrictions or better data. We also discuss results on discrimination between alternative models of oligopoly competition.