For any infinite discrete group G, we will discuss the foundations of the proper G-equivariant stable homotopy theory. This is a joint work with Degrijse, Hausmann, Lueck and Schwede. After setting up the foundations, we will talk about the connections to geometric group theory and finiteness properties of groups. In particular, we will introduce the notion of stable geometric dimension of a discrete group G and show that if G is virtually torsion free, then this dimension coincides with the virtual cohomological dimension of G. The latter is joint with Barcenas and Degrijse.