More than 30 years ago, the feasibility of detecting magnetic resonance in the Faraday-rotation noise spectrum of transmitted light was demonstrated experimentally. However, practical applications of this experimental approach have emerged only recently thanks, in particular, to a number of crucial technical advancements. This method has now become a popular and efficient tool for studying magnetic resonance and spin dynamics in atomic and solid-state paramagnets. In this paper, we present a review of research in the field of spin-noise spectroscopy, including its physical basis, its evolution since its first experimental demonstration, and its recent experimental advances. Main attention is paid to the specific capabilities of this technique that render it unique compared to other methods of magnetic and optical spectroscopy. The paper is primarily intended for experimentalists who may wish to use this novel optical technique.