We analyze recent contributions to growth theory based on the model of expanding variety of Romer (1990). In the first part, we present different versions of the benchmark linear model with imperfect competition. These include the “labequipment” model, labor-for-intermediates” and “directed technical change”. We review applications of the expanding variety framework to the analysis of international technology diffusion, trade, cross-country productivity differences, financial development and fluctuations. In many such applications, a key role is played by complementarities in the process of innovation.