Goodwillie calculus and model structures

We report on joint work with O. Röndigs. We construct model structures and Quillen equivalences that capture many notions in Goodwillie's calculus of functors between certain pointed simplicial model categories, such as n-excisive, n-homogeneous homotopy functors, cross effects and derivatives. At the end, I will mention two ongoing projects, one joint with Dwyer/Röndigs and the other with C. Berger.