Darwin's idea of evolution by natural selection is almost universally accepted by biologists, but debate continues about the units of selection. The history of this debate starts with Wynne-Edwards' arguments for group selection, and Hamilton's explantation of social behaviour in terms of the inclusive fitness of individuals. Hamilton's approach differs from the gene-centred approach pioneered by Williams and Dawkins, although both the problem and its solution are essentially the same. The choice of approach depends on conceptual and mathematical simplicity, and on one's attitude to the causal efficacy of genes. The problem of selection on units above the species level is discussed. Today, we are in the main concerned with cases in which selection acts simultaneously at two levels. This is true of current research on intragenomic conflict and of the suggestion by Maynard Smith and Szathmáry that in the major transitions in evolution, entities that were capable of independent replication before the transition can only replicate as part of a larger whole after it.