  We study the dynamics of black holes in Einstein-scalar-Gauss-Bonnet theories
that exhibit spontaneous black hole scalarization using recently introduced
methods for solving the full, non-perturbative equations of motion. For one
sign of the coupling parameter, non-spinning vacuum black holes are unstable to
developing scalar hair, while for the other, instability only sets in for black
holes with sufficiently large spin. We study scalarization in both cases,
demonstrating that there is a range of parameter space where the theory
maintains hyperbolic evolution and for which the instability saturates in a
scalarized black hole that is stable without symmetry assumptions. However,
this parameter space range is significantly smaller than the range for which
stationary scalarized black hole solutions exist. We show how different choices
for the subleading behavior of the Gauss-Bonnet coupling affect the dynamics of
the instability and the final state, or lack thereof. Finally, we present
mergers of binary black holes and demonstrate the imprint of the scalar hair in
the gravitational radiation.
