Research in the field of laser thermonuclear fusion, which began more than 60 years ago at the P.N. Lebedev Physical Institute, in 2022 led to a record result in igniting a controlled fusion reaction in a laboratory experiment. The article outlines the modern concept of laser thermonuclear fusion and the most significant results of research of pulsed plasma with an extremely high energy density formed, when powerful laser radiation affects matter. A concise summary is presented of the history of laser thermonuclear fusion research, in which special attention is paid to the role of the P.N. Lebedev Physical Institute.