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The idea of exciton condensation in solids was introduced in 1960's with theanalogy to superconductivity in mind. While exciton supercurrents have beenrealized only in artificial quantum-well structures so far, the application ofthe concept of excitonic condensation to bulk solids leads to a rich spectrumof thermodynamic phases with diverse physical properties. In this review wediscuss recent developments in the theory of exciton condensation in systemsdescribed by Hubbard-type models. In particular, we focus on the connections totheir 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' whichwould allow the reader to efficiently combine results obtained in thesedifferent fields.

Excitonic condensation in systems of strongly correlated electrons