  We discuss several arithmetic aspects of Bianchi groups, especially from a
computational point of view. In particular, we consider computing the homology
of Bianchi groups together with the Hecke action, connections with automorphic
forms, abelian varieties, Galois representations and the torsion in the
homology of Bianchi groups. Along the way, we list several open problems and
conjectures, survey the related literature, presenting concrete examples and
numerical data.
