In this thesis, we will relax two major assumptions in economic growth theory. First of all, we will study growth models with eterogeneous capital goods, the so called vintage capital models: technological advances are not incorporated in all generations of capital goods and there is an optimal age distribution of the capital stocks. We will devote the three first chapters of this thesis to this class of models. Several lessons on technology diffusion will be extracted, notably in connection with the nowadays hot debate on energy saving, technology progress, growth and environmental policy. Secondly, we will introduce explicitly the geographical dimension to the neoclassical growth models, which allow us to build a new class of models. We call them geographic growth models. In this framework, we will identify the consequences of capital mobility across space. In particular, we will examine the optimal stationary distribution of capital across space. Under this framework, we could (i) study the continuous space structure, and (ii) allow capital accumulation.