  The idea of exciton condensation in solids was introduced in 1960's with the
analogy to superconductivity in mind. While exciton supercurrents have been
realized only in artificial quantum-well structures so far, the application of
the concept of excitonic condensation to bulk solids leads to a rich spectrum
of thermodynamic phases with diverse physical properties. In this review we
discuss recent developments in the theory of exciton condensation in systems
described by Hubbard-type models. In particular, we focus on the connections to
their various strong-coupling limits that have been studied in other contexts,
e.g., cold atoms physics. One of our goals is to provide a 'dictionary' which
would allow the reader to efficiently combine results obtained in these
different fields.
