Abstract We provide an overview and synthesis of recent work on models of monopolistic competition with heterogeneous firms in international trade, paying particular attention to competition effects, pass-through, selection effects, and linking distributions of firm characteristics and outcomes. A recurring theme is that CES preferences are extremely convenient for deriving analytic results, but also extremely restrictive in their theoretical and empirical implications. We introduce the class of “constant-response demand functions” to describe some related families of demand functions that provide a unifying principle for much recent work that explores alternatives to CES demands.