Poynting vector singularities are considered for scalar and vector fields. The behavior of averaged and instantaneous components is analyzed. The relationships between Poynting singularities and conventional optical ones, other special sets of electromagnetic fields are established. The elementary topological regularities and reactions are formulated. The results of computer simulation are presented.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.