This talk will be an introduction to the enumeration of combinatorial types of convex polytopes, and the contrast between low and high dimensions. While in dimensions up to 3 we have a very good understanding on the asymptotic growth of the number of polytopes with respect to the number of vertices, in higher dimensions we only have coarse estimates. There is a family for which precise enumeration is possible, d-polytopes with d+3 vertices, thanks to Gale duality. I will finish with open problems and partial results concerning the enumeration of d-polytopes in terms of their number of vertices and facets.