A fascinating property of bosons, quantum particles with integer spin, is their ability to massively occupy a single quantum state. In this regime, the cloud of bosons behave as a macroscopic coherent ensemble with non-linear properties emerging from interactions. So far most experiments have focused on the physics of closed systems such as isolated clouds of cold atoms. The phase diagram of closed BEC has been explored and shown very rich physics with universal statistical properties and scaling laws. Recently a novel class of BEC has been considered, where the system is open and constantly loses particles via dissipative process. To reach a steady state, dissipation needs to be compensated via pumping so that the condensate shows out of equilibrium dynamics. Interestingly the openness of the system fundamentally changes the physics of the BEC and many open questions need to be addressed both theoretically and experimentally: what are the statistical properties of open BECs? What universal scaling laws can be identified? How is the coherence affected by drive and dissipation? In this project, we propose to explore this physics using BECs made of photons in optical cavities.