  I describe the general mathematical construction and physical picture of
topological black holes, which are black holes whose event horizons are
surfaces of non-trivial topology. The construction is carried out in an
arbitrary number of dimensions, and includes all known special cases which have
appeared before in the literature. I describe the basic features of massive
charged topological black holes in $(3+1)$ dimensions, from both an exterior
and interior point of view. To investigate their interiors, it is necessary to
understand the radiative falloff behaviour of a given massless field at late
times in the background of a topological black hole. I describe the results of
a numerical investigation of such behaviour for a conformally coupled scalar
field. Significant differences emerge between spherical and higher genus
topologies.
