Optical microcavities and waveguides coupled to diamond are needed to enable efficient communication between quantum systems such as nitrogen-vacancy centers which are known already to have long electron spin coherence lifetimes. This paper describes recent progress in realizing microcavities with low loss and small mode volume in two hybrid systems: silica microdisks coupled to diamond nanoparticles, and gallium phosphide microdisks coupled to single-crystal diamond. A theoretical proposal for a gallium phosphide nanowire photonic crystal cavity coupled to diamond is also discussed. Comparing the two material systems, silica microdisks are easier to fabricate and test. However, at low temperature, nitrogen-vacancy centers in bulk diamond are spectrally more stable, and we expect that in the long term the bulk diamond approach will be better suited for on-chip integration of a photonic network.