  An ordered state of electrons in solids in which excitons condense was
proposed many years ago as a theoretical possibility but has, until recently,
never been observed. We review recent studies of semiconductor bilayer systems
that provide clear evidence for this phenomenon and explain why exciton
condensation in the quantum Hall regime, where these experiments were
performed, is as likely to occur in electron-electron bilayers as in
electron-hole bilayers. In current quantum Hall exciton condensates, disorder
induces mobile vortices that flow in response to a supercurrent and limit the
extremely large bilayer counterflow conductivity.
