It has been established, on the perturbative level, that rotating black holes are prone to the superradiant instability in the presence of low-frequency, light bosonic fields. It is, however, an entirely open question what the endstate of the instability is when non-linear interactions and backreaction onto the spacetime geometry are taken into account, when these effects become important and what their potentially observable signatures are. We have started to investigate these open issues in the context of massive vector fields, and I will give a status report on our latest results.