Hamilton’s theory of inclusive fitness showed how natural selection could lead to behaviors that decrease the relative fitness of the actor and also either benefit (altruism) or harm (spite) other individuals. However, several fundamental issues in the evolution of altruism and spite have remained contentious. Here, we show how recent work has resolved three key debates, helping clarify how Hamilton’s theoretical overview links to real-world examples, in organisms ranging from bacteria to humans: Is the evolution of extreme altruism, represented by the sterile workers of social insects, driven by genetics or ecology? Does spite really exist in nature? And, can altruism be favored between individuals who are not close kin but share a “greenbeard” gene for altruism?