Excitonic condensation in systems of strongly correlated electrons

The idea of exciton condensation in solids was introduced in the 1960s with the analogy of superconductivity in mind. While exciton supercurrents have been realised 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' that would allow the reader to efficiently combine results obtained in these different fields.