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.