Hetero n-i-p-i crystals are periodic arrays of n- and p-doped layers with interspersed undoped (i-) layers of a different, smaller band gap semiconductor. They combine the interesting and useful tunability of conventional doping superlattices ("n-i-p-i crystals") with the only weakly broadened subhand structure of modulation-doped hetero-structure superlattices. Two different versions of such superlattices will be discussed. The first temperature-, intensity-, and time-dependent luminescence measurements on "type-II hetero n-i-p-i's" confirm the expected fine structure of the luminescence spectra. New non-linear optical phenomena like absorption oversaturation are predicted for "type-I hetero n-i-p-i's".