Luck egalitarianism is a family of egalitarian theories of distributive justice that aim to counteract the distributive effects of luck. This article explains luck egalitarianism's main ideas, and the debates that have accompanied its rise to prominence. There are two main parts to the discussion. The first part sets out three key moves in the influential early statements of Dworkin, Arneson, and Cohen: the brute luck/option luck distinction, the specification of brute luck in everyday or theoretical terms and the specification of advantage as resources, welfare, or some combination of these. The second part covers three later developments: the democratic egalitarian critique of luck egalitarianism, the luck egalitarian acceptance of pluralism, and luck egalitarian doubts about the significance of the brute luck/option luck distinction.