This paper presents a New Economic Geography model of structural change, agglomeration and growth. Assuming a non-homothetic preference structure, our results show that a progressive reduction of trade costs allows the economy to pass from a pre-industrialized to an industrialized stage and then, within the latter, from a dispersed to an urbanized regime. However, the introduction of capital accumulation and the dynamic setting of our model opens the door to a richer set of implications. First, an additional stage is introduced as, for some intermediate values of trade costs, a multiple equilibria regime emerges with simultaneously stable symmetric and core-periphery equilibria. Second, the introduction of non-homotheticity introduces a new channel through which growth is affected by trade costs and agglomeration. In particular, integration is always growth-enhancing while agglomeration is growth-detrimental.