This chapter describes new developments in the understanding of the luminescence of complexes consisting of a central highly-charged transition metal ion without d electrons surrounded by a number of oxygen ions (usually 4 or 6 in a tetrahedral or octahedral arrangement, respectively). Examples are titanates, vanadates, molybdates and tungstates. Recently results from low-temperature measurements have become available. On the other hand reliable molecular-orbital calculations have been performed. These are compared with each other. It is possible to obtain from the luminescence data information on the splitting of energy levels due to crystal-field and spin-orbit interactions. It is stressed that still a lot of data are lacking and that considerable effort has to be made to obtain a complete picture. Also the influence of ions with s2 configuration (Pb2+ Bi3+) on these complexes is considered.