In this talk, I will present some of our recent theoretical results concerning photons in a coupled cavity array under a synthetic magnetic field. A suitable coupling of the propagation and polarization degrees of freedom introduces a geometrical phase for photons tunneling between adjacent sites of a coupled cavity array, which gives rise to the artificial field. I will discuss the feasibility of observing strong magnetic field effects in the optical spectra of realistic systems, including the Hofstadter butterfly spectrum. I will also touch on the observability of a fractional quantum Hall effect for photons in these systems, which is expected to appear when effective interactions are induced between photons.