Bose-Einstein Condensation of Excitons in Cu$_2$O: Progress Over Thirty Years

Experiments on Bose-Einstein condensation (BEC) of excitons in the semiconductor Cu$_2$O started over thirty years ago, as one of the first serious attempts at exciton BEC. Early claims were based on spectroscopic signatures and transport data which have since been reinterpreted, in large part because the Auger recombination process for excitons was not well understood. Understanding of the Auger process has also advanced, and recent experiments have made significant progress toward exciton BEC. We review the history of experiments on exciton BEC in Cu$_2$O, the Auger recombination process, and the prospects for observing exciton BEC in this system in the near future.