We shall examine the impact of Charles S. Elton's 1924 article on periodic fluctuations in animal populations on the development of modern population ecology. We argue that his impact has been substantial and that during the past 75 years of research on multi-annual periodic fluctuations in numbers of voles, lemmings, hares, lynx and game animals he has contributed much to the contemporary understanding of the causes and consequences of population regulation. Elton was convinced that the cause of the regular fluctuations was climatic variation. To support this conclusion, he examined long-term population data then available. Despite his firm belief in a climatic cause of the self-repeating periodic dynamics which many species display, Elton was insightful and far-sighted enough to outline many of the other hypotheses since put forward as an explanation for the enigmatic long-term dynamics of some animal populations. An interesting, but largely neglected aspect in Elton's paper is that it ends with speculation regarding the evolutionary consequences of periodic population fluctuations. The modern understanding of these issues will also be scrutinised here. In population ecology, Elton's 1924 paper has spawned a whole industry of research on populations displaying multi-annual periodicity. Despite the efforts of numerous research teams and individuals focusing on the origins of multi-annual population cycles, and despite the early availability of different explanatory hypotheses, we are still lacking rigorous tests of some of these hypotheses and, consequently, a consensus of the causes of periodic fluctuations in animal populations. Although Elton would have been happy to see so much effort spent on cyclic populations, we also argue that it is unfortunate if this focus on a special case of population dynamics should distract our attention from more general problems in population and community dynamics.