This paper analyzes the role of complexity in production on the level of output and on its rate of growth. We develop an endogenous growth model with human capital accumulation, where increased complexity could exert either a positive or a negative effect on the level of output but always a positive effect on its rate of growth. Our empirical measure of complexity is derived from net trade flows, and is based on the product space description of production sectors in the global economy. The evidence from a broad cross-section of countries is consistent with the main theoretical predictions of the model, and supports the view that production complexity is important in order to account for differences in economic performance. An indicator of the intensity of vertical trade among countries is also shown to be relevant to explain output performance