Arithmetic groups --- that generalize the modular group --- can have'a lot' of torsion in their homology. Starting from the examples of congruence subgroups of the modular and Bianchi groups where homology reduces to abelianization, I will explain what 'a lot' means. I will then try to explain how this interacts with more classical question of number theory and geometry. This is joint work with Akshay Venkatesh and Mehmet Haluk Sengun.