I have been computing the K-theory of foliation C*-algebras on some specific examples, which are easy to visualise, especially in the case of the 3-torus. On the other hand, I have been studying some characteristic classes of foliations, in particular the Godbillon-Vey invariant, and seen how they can be expressed as cyclic cocycles on the foliation C*-algebra. This work is related to Connes'index theorem and to the Novikov conjecture.