This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a full and complete 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka a nanobox for light), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate all known photonic crystal structures with a demonstrated 3D band gap.
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