  A Reissner-Nordstr\"om black hole (BH) is superradiantly unstable against
spherical perturbations of a charged scalar field, enclosed in a cavity, with
frequency lower than a critical value. We use numerical relativity techniques
to follow the development of this unstable system -- dubbed a charged BH bomb
-- into the non-linear regime, solving the full Einstein--Maxwell--Klein-Gordon
equations, in spherical symmetry. We show that: $i)$ the process stops before
all the charge is extracted from the BH; $ii)$ the system settles down into a
hairy BH: a charged horizon in equilibrium with a scalar field condensate,
whose phase is oscillating at the (final) critical frequency. For low scalar
field charge, $q$, the final state is approached smoothly and monotonically.
For large $q$, however, the energy extraction overshoots and an explosive
phenomenon, akin to a $bosenova$, pushes some energy back into the BH. The
charge extraction, by contrast, does not reverse.
