Three-dimensional (3D) photonic crystals with a 3D photonic bandgap play a fundamental role in cavity quantum electrodynamics (QED), especially in phenomena where the local density of optical states is essential. We first review the current status of the fabrication of 3D photonic crystals with a bandgap at optical frequencies, corresponding to wavelengths below 2500 nm. We discuss the main implications of 3D bandgaps for cavity QED, in particular spontaneous emission inhibition of emitters embedded in a 3D bandgap crystal. Moreover, we review progress in enhanced emission of emitters placed in a photonic bandgap cavity, thresholdless laser action in a miniature photonic crystal cavity, breaking of the weak-couping limit of cavity QED. Finally, we discuss several exciting applications of 3D photonic band gap crystals, namely the shielding of decoherence for quantum information science, the manipulation of multiple coupled emitters including resonant energy transfer, lighting, and possible spin-off to 3D nanofabrication for future high-end computing.