  Complex braid groups are the natural generalizations of braid groups
associated to arbitrary (finite) complex reflection groups. We investigate
several methods for computing the homology of these groups. In particular, we
get the Poincar\'e polynomial with coefficients in a finite field for one large
series of such groups, and compute the second integral cohomology group for all
of them. As a consequence we get non-isomorphism results for these groups.
