Stable colloidal solutions of zinc oxide in dimethylsulfoxide were synthesized via interaction between zinc(II) acetate and tetraalkylammonium hydroxides (alkyl-ethyl, propyl, butyl, and pentyl). Colloids of ZnO emit photoluminescence in a broad band with a maximum at 2.3-2.4 eV with quantum yields of up to 9-10% at room temperature and 15-16% at 80 K. The photoluminescence is supposed to originate from the radiative recombination of conduction band electrons with holes captured by deep traps having corresponding states in the band gap 1.0-1.2 eV above the valence band edge. The size of colloidal ZnO nanocrystals depends on the duration and temperature of the post-synthesis treatment and varies in the range of 3-6 nm. Growth of the ZnO nanocrystals can be terminated at any moment of the thermal treatment by freezing the colloidal solution or by addition of tetraethyl orthosilicate which hydrolyses forming core-shell ZnO@SiO2 particles. ZnO nanocrystals introduced into polyethyleneimine films can be used as an active component of an LED emitting at an applied voltage higher than 13 V.