  The new, rapidly developing field of theoretical research --- studies of dark
energy interacting with black holes (and, in particular, accreting onto black
holes) --- is reviewed. The term `dark energy' is meant to cover a wide range
of field theory models, as well as perfect fluids with various equations of
state, including cosmological dark energy. Various accretion models are
analyzed in terms of the simplest test field approximation or by allowing back
reaction on the black-hole metric. The behavior of various types of dark energy
in the vicinity of Schwarzschild and electrically charged black holes is
examined. Nontrivial effects due to the presence of dark energy in the black
hole vicinity are discussed. In particular, a physical explanation is given of
why the black hole mass decreases when phantom energy is being accreted, a
process in which the basic energy conditions of the famous theorem of
nondecreasing horizon area in classical black holes are violated. The
theoretical possibility of a signal escaping from beneath the black hole event
horizon is discussed for a number of dark energy models. Finally, the violation
of the laws of thermodynamics by black holes in the presence of noncanonical
fields is considered.
