Soddy's report of 1917, in which he maintained that experimental data indicated the existence of nuclear isomers, turned out to be erroneous. The first true case of nuclear isomerism was discovered by Hahn in 1921. However, the only known example of nuclear isomerism that was available for a very long time ($^{234}$Pa) had an extremely complicated level and transition scheme, which meant that it was impossible to establish the essence of the phenomenon. It was only after the discovery of artifical radioactivity that extensive experimental data were published and, on this basis, further research into nuclear isomerism proceeded exceedingly rapidly. Important stages in the history of research into nuclear isomerism were the identification of several cases of ``an excessive number of half-lives'' among artificial radioactive nuclides (In, Br, Rh), the development of theoretical descriptions of nuclear isomerism (G. Gamow, C.F. Weizs\"acker, and H.A. Bethe), unambiguous demonstration of the fact that, in the case of radiobromine, the ``carrier'' of the two different half-lives was 80Br, experiments designed to confirm the various suggested hypotheses, and the achievement of a complete understanding of the essence of nuclear isomerism. In this review, early work is discussed from the modern point of view. The importance of the work carried out by the group headed by I. V. Kurchatov on the nature of nuclear isomerism is emphasized.