  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.
