Cavity QED systems often contain many interacting degrees of freedom, but they are unlike traditional many-body systems for two main reasons. First, the mediation of interactions through a single cavity mode promotes collective behavior, often enabling accurate mean-field descriptions. Second, they are driven and dissipative, and therefore one should not in general expect to find them in thermal equilibrium. While the first difference makes them simpler than traditional many-body systems, the second makes them considerably richer and more complicated. Recent advances in fabricating cavity QED systems with short-range interactions are enabling experimental explorations of well-controlled non-equilibrium quantum systems that are not well described by mean-field theory. I will discuss some recent theoretical work on a canonical model capturing this (relatively) poorly understood scenario, the driven-dissipative Bose-Hubbard model. Amongst many surprising behaviors, we find that equilibration is harder to avoid than one might expect --- even though this model is built to prevent it, thermal equilibrium emerges anyway.