Experimental research on photonuclear reactions with gamma beams of intermediate energy (from the meson photoproduction threshold up to several GeV) produced by laser photons Compton backscattered on electrons (positrons) circulating in storage rings is reviewed. Common to all of the studies are the subject (interaction mechanisms of gamma-quanta with nuclei) and the experimental technique (Compton beams), which has come to be widely used in recent years. The experimental and applied possibilities offered by the high-intensity Compton beams created in recent years are also discussed.