  Coherent interfaces between optical photons and long-lived matter qubits form
a key resource for a broad range of quantum technologies. Cavity quantum
electrodynamics (cQED) offers a route to achieve such an interface by enhancing
interactions between cavity-confined photons and individual emitters. Over the
last two decades, a promising new class of emitters based on defect centers in
diamond have emerged, combining long spin coherence times with atom-like
optical transitions. More recently, advances in optical resonator technologies
have made it feasible to realize cQED in diamond. This article reviews progress
towards coupling color centers in diamond to optical resonators, focusing on
approaches compatible with quantum networks. We consider the challenges for
cQED with solid-state emitters and introduce the relevant properties of diamond
defect centers before examining two qualitatively different resonator designs:
micron-scale Fabry-Perot cavities and diamond nanophotonic cavities. For each
approach, we examine the underlying theory and fabrication, discuss strengths
and outstanding challenges, and highlight state-of-the-art experiments.
