  In general relativity, astrophysical black holes are simple objects, being
described by just their mass and spin. These simple solutions are not exclusive
to general relativity, as they also appear in theories that allow for an extra
scalar degree of freedom. Recently, it was shown that some theories which
couple a scalar field with the Gauss-Bonnet invariant can have the same classic
general relativity black hole solutions as well as hairy black holes. These
scalarized solutions can be stable, having an additional "charge" term that has
an impact on the gravitational-wave emission by black hole binaries. In this
paper, we overview black hole solutions in scalar-Gauss-Bonnet gravity,
considering self-interacting terms for the scalar field. We present the mode
analysis for the mono and dipolar perturbations around the Schwarzschild black
hole in scalar-Gauss-Bonnet, showing the transition between stable and unstable
solutions. We also present the time-evolution of scalar Gaussian wave packets,
analyzing the impact of the scalar-Gauss-Bonnet term in their evolution. We
then present some scalarized solutions, showing that nonlinear coupling
functions and self-interacting terms can stabilize them. Finally, we compute
the light-ring frequency and the Lyapunov exponent, which possibly estimate the
black hole quasinormal modes in the eikonal limit.
