Soon after research on molecular scattering of light began in the Soviet Union, Landsberg and Mandel'shtam made one of the most important discoveries in physics in this century: combinational scattering of light (or the ``Raman effect'', as it is known outside the Soviet Union. Transl. ed. note). In this paper, the history of Soviet research on this subject is briefly outlined. Research in other countries is discussed only briefly and only to the extent necessary for an objective description of the course of events. Use is made of archival material, including one of the first spectrograms obtained by Landsberg and Mandel'shtam that has been preserved, which clearly shows a combinational-scattering line. This spectrogram, obtained on February 23--24, 1928, constituted the first observation of the new effect anywhere, but the results were published only with considerable delay. Translations into Russian of the complete texts of the first papers on the subject by Raman and Krishnan and by Landsberg and Mandel'shtam are presented (only the references to original papers are given in the English edition). Some early descriptions of the effect and some early comments on it (by Born, Rutherford, etc.) are given. Current trends in the development and applications of combinational scattering are outlined very briefly at the end of the paper.