I will give an overview over basic features of equivariant coarse homotopy theory. Thereby the emphasis is put on facts and arguments which hold for arbitrary coarse homology theories. I will indicate applications of the theory to the study of assembly maps. All this applies in particular to the topological coarse K-homology with coefficients in a C*-category.

I will indicate which constructions with C*-categories and which properties of the K-theory functor for C*-categories are used.