Lück's approximation theorem says that the L2–Betti numbers of a residually finite group measure the rational homological growth of residual sequences of finite index normal subgroups. One can then ask about mod p homology growth or growth of torsion in integral homology. I will give complete calculations of these for right-angled Artin groups, and mention some consequences. This is joint work with Grigori Avramidi and Boris Okun.