Abstract: Coarse spaces, first introduced by J. Roe for studying index-type theorems, have recently found applications also in K-theory and assembly map conjectures. The main tool in such applications is given by coarse homology theories, homological invariants of coarse spaces. Goal of the talk is to define coarse homology theories using the homotopical approach developed by U. Bunke and A. Engel.  The main example will be coarse algebraic K-theory.