Much of the philosophical literature on health inequalities seeks to establish the superiority of one or another conception of luck egalitarianism. In recent years, however, an increasing number of self-avowed egalitarian philosophers have proposed replacing luck egalitarianism with alternatives that stress the moral relevance of distinct relationships, rather than the moral relevance of good or bad luck. After briefly explaining why I am not attracted to luck egalitarianism, I seek in this chapter to distinguish and clarify three views that have (...) been characterized in the philosophical literature as forms of relational egalitarianism. I call these three relational views equality of treatment, equality of concern, and social egalitarianism. I will explain why each claims to be a form of egalitarianism and why these three views should not be seen as competitors. I will argue that each brand of relational egalitarianism describes a plausible plank of distributive justice that bears on the evaluation of health inequalities and on the political institutions that create, sustain, or exacerbate them. To illustrate this pluralistic relational egalitarian approach, I will draw on a case study by Horton and Barker (this volume) to discuss how each of the three planks might be brought to bear on the evaluation of oral health disparities among the children of migrant Latino farmworkers in California. (shrink)