The latest results obtained from investigating vector correlations in the photodissociation of di- and triatomic molecules are reviewed. Expressions for the polarization moments of atoms formed as a result of the photodissociation of an arbitrary molecule by polarized radiation, which depend on spatial and spin variables, are presented. The set of anisotropy parameters, which can be determined experimentally and then utilized to obtain a complete quantum-mechanical description of the primary photodissociation act, is discussed. Two methods for determining the orientation parameters, alignment parameters, and higher polarization moments of atomic photofragments are considered. They are based on a) ion imaging, which involves laser photoionization followed by mass-spectrometric detection of the photofragments and b) sub-Doppler laser polarization spectroscopy of the photofragments. The results of an experimental study of the photodissociation of Cl-2 molecules, which leads to the formation of Cl(P-2(3/2)) atoms with aligned electronic angular momenta, are presented as an example. (C) 1999 American Institute of Physics. [S1063-7842(99)01009-0].