  The advent of controlled experimental accessibility of Bose-Einstein
condensates, as realized with e.g. cold atomic gases, exciton-polaritons, and
more recently photons in a dye-filled optical microcavity, has paved the way
for new studies and tests of a plethora of fundamental concepts in quantum
physics. We here describe recent experiments studying a transition between
laser-like dynamics and Bose-Einstein condensation of photons in the dye
microcavity system. Further, measurements of the second-order coherence of the
photon condensate are presented. In the condensed state we observe photon
number fluctuations of order of the total particle number, as understood from
effective particle exchange with the photo-excitable dye molecules. The
observed intensity fluctuation properties give evidence for Bose-Einstein
condensation occurring in the grand-canonical statistical ensemble regime.
