A survey of current issues concerning the electronic and optical properties of HgTe-CdTe superlattices is given. The superlattice has been conjectured to provide certain advantages relative to the HgCdTe alloy for infrared detectors. A comparison of theoretical predictions with recent measurements is made. The conduction electrons are expected to be partially localized near the HgTe-CdTe interfaces, to a degree dependent on the superlattice band gap. The valence band offset between HgTe and CdTe is still not determined precisely. Measurements of the optical absorption coefficient as a function of photon energy indicates that expected structure due to energy subbands does occur, indicating the presence of abrupt interfaces. Recent measurements of resonant tunneling currents through double barrier structures also imply abrupt interfaces, and may help in determining the valence band offset.