We present an overview of the theoretical background and experimental re- sults in the rapidly developing field of semiconductor quantum dots - systems 8 6 of dimensions as small as 10- -10- m (quasi-zero-dimensional) that contain a small and controllable number (1-1000) of electrons. The electronic structure of quantum dots, including the energy quan- tization of the single-particle states (due to spatial confinement) and the evolution of these (Fock-Darwin) states in an increasing external magnetic field, is described. The properties of many-electron systems confined in a dot are also...