I will discuss several regimes that appear in aggregation diffusion problems with homogeneous kernels. I will first discuss recent results concerning the radial symmetry and long time asymptotics in the diffusion dominated case. Then I will concentrate in the fair competition case distinguishing among porous medium like cases and fast diffusion like ones. I will discuss the main qualitative properties in terms of stationary states and minimizers of the free energies. In particular, all the porous medium cases are critical while the fast diffusion are not. This talk is based on works in collaboration with S. Hittmeir, B. Volzone, and Y. Yao; and with V. Calvez and F. Hoffmann.