Many thought Darwinian natural selection could not explain altruism. This error led Wynne-Edwards to explain sustainable exploitation in animals by selection against overexploiting groups. Williams riposted that selection among groups rarely overrides within-group selection. Hamilton showed that altruism can evolve through kin selection. How strongly does group selection influence evolution? Following Price, Hamilton showed how levels of selection interact: group selection prevails if Hamilton's rule applies. Several showed that group selection drove some major evolutionary transitions. Following Hamilton's lead, Queller extended Hamilton's rule, replacing genealogical relatedness by the regression on an actor's genotypic altruism of interacting neighbours' phenotypic altruism. Price's theorem shows the generality of Hamilton's rule. All instances of group selection can be viewed as increasing inclusive fitness of autosomal genomes. Nonetheless, to grasp fully how cooperation and altruism evolve, most biologists need more concrete concepts like kin selection, group selection and selection among individuals for their common good.