Photons in the energy range of about one-half to several GeV have been proposed as a signal of the formation of a quark-gluon plasma in high-energy collisions. To lowest order the thermal emission rate is infrared divergent for massless quarks, but we regulate this divergence using the resummation technique of Braaten and Pisarski. Photons can also be produced in the hadron phase. We find that the dominant contribution comes from the reactions ππ-->ργ and πρ-->πγ the decays ω-->πγ and ρ-->ππγ are also significant. Comparing the thermal emission rates at a temperature T=200 MeV we conclude that the hadron gas shines just as brightly as the quark-gluon plasma.