  We review recent experiments on the Bose-Einstein condensation of photons in
a dye-filled optical microresonator. The most well-known example of a photon
gas, photons in blackbody radiation, does not show Bose-Einstein condensation.
Instead of massively populating the cavity ground mode, photons vanish in the
cavity walls when they are cooled down. The situation is different in an
ultrashort optical cavity imprinting a low-frequency cutoff on the photon
energy spectrum that is well above the thermal energy. The latter allows for a
thermalization process in which both temperature and photon number can be tuned
independently of each other or, correspondingly, for a non-vanishing photon
chemical potential. We here describe experiments demonstrating the
fluorescence-induced thermalization and Bose-Einstein condensation of a
two-dimensional photon gas in the dye microcavity. Moreover, recent
measurements on the photon statistics of the condensate, showing Bose-Einstein
condensation in the grandcanonical ensemble limit, will be reviewed.
