  Recently a new type of system exhibiting spontaneous coherence has emerged --
the exciton-polariton condensate. Exciton-polaritons (or polaritons for short)
are bosonic quasiparticles that exist inside semiconductor microcavities,
consisting of a superposition of an exciton and a cavity photon. Above a
threshold density the polaritons macroscopically occupy the same quantum state,
forming a condensate. The lifetime of the polaritons are typically comparable
to or shorter than thermalization times, making them possess an inherently
non-equilibrium nature. Nevertheless, they display many of the features that
would be expected of equilibrium Bose-Einstein condensates (BECs). The
non-equilibrium nature of the system raises fundamental questions of what it
means for a system to be a BEC, and introduces new physics beyond that seen in
other macroscopically coherent systems. In this review we focus upon several
physical phenomena exhibited by exciton-polariton condensates. In particular we
examine topics such as the difference between a polariton BEC, a polariton
laser, and a photon laser, as well as physical phenomena such as superfluidity,
vortex formation, BKT (Berezinskii-Kosterlitz-Thouless) and BCS
(Bardeen-Cooper-Schrieffer) physics. We also discuss the physics and
applications of engineered polariton structures.
