Like altruism, mutualism, cooperation between species, evolves only by enhancing all participants’ inclusive fitness. Mutualism evolves most readily between members of different kingdoms, which pool complementary abilities for mutual benefit: some of these mutualisms represent major evolutionary innovations. Mutualism cannot persist if cheating annihilates its benefits. In long‐term mutualisms, symbioses, at least one party associates with the other nearly all its life. Usually, a larger host harbours smaller symbionts. Cheating is restrained by vertical transmission, as in Buchnera; partner fidelity, as among bull‐thorn acacias and protective ants; test‐based choice of symbionts, as bobtail squid choose bioluminescent bacteria; or sanctioning nonperforming symbionts, as legumes punish nonperforming nitrogen‐fixing bacteria. Mutualisms involving brief exchanges, as among plants and seed‐dispersers, however, persist despite abundant cheating. Both symbioses and brief‐exchange mutualisms have transformed whole ecosystems. These mutualisms may be steps towards ecosystems which, like Adam Smith’s ideal economy, serve their members’ common good.