  In the context of $f(R)$ gravity theories, the issue of finding static and
spherically symmetric black hole solutions is addressed. Two approaches to
study the existence of such solutions are considered: first, constant curvature
solutions, and second, the general case (without imposing constant curvature)
is also studied. Performing a perturbative expansion around the
Einstein-Hilbert action, it is found that only solutions of the
Schwarzschild-(Anti-) de Sitter type are present (up to second order in
perturbations) and the explicit expressions for these solutions are provided in
terms of the $f(R)$ function. Finally we consider the thermodynamics of black
holes in Anti-de Sitter space-time and study their local and global stability.
