  The classic black hole mechanics and thermodynamics are formulated for
stationary black holes with event horizons. Alternative theories of gravity of
interest for cosmology contain a built-in time-dependent cosmological
"constant" and black holes are not stationary. Realistic black holes are anyway
dynamical because they interact with astrophysical environments or, at a more
fundamental level, because of backreaction by Hawking radiation. In these
situations the teleological concept of event horizon fails and apparent or
trapping horizons are used instead. Even as toy models, black holes embedded in
cosmological "backgrounds" and other inhomogeneous universes constitute an
interesting class of solutions of various theories of gravity. We discuss the
known phenomenology of apparent and trapping horizons in these geometries,
focusing on spherically symmetric inhomogeneous universes.
