Determining the nature of dark matter (DM) is one of the most important challenges of modern experimental physics. This article overviews the major arguments confirming the existence of DM, gives a modern classification of DM particles, identifies possible candidates for their role, discusses the most significant DM particle search experiments conducted and under development. The publication mainly aims to give an idea of diverse experimental methods of and approaches to the registration of DM particles, as well as of the currently available results of their search, which open new prospects in DM studies and contribute to solving topical problems of New Physics.