Solving the puzzle of resilient inequality requires coming to grips with how higher-than-desirable levels of inequality have come to be reproduced in so many of the rich democracies simultaneously. In Chapter 1, I showed that the normal explanations for this phenomenon offered by political science and economic theories fall short, and took the first steps toward laying out an alternative argument. In this chapter, I make a more comprehensive case for my claim that political solutions to the problem of inequality are shaped both by legacies of the past and by the way politicians talk about the problem of inequality in the present. As the central institutions for containing the growth of inequality in the welfare regimes of the postwar period collided, beginning in the 1980s, with a rising neoliberal economic policy paradigm, politicians on the center-left responded by changing how they framed the issue of inequality. This shift in framing had unanticipated consequences, however: instead of making the problem of inequality more politically tractable, as politicians hoped, the new framing of inequality as a matter of health made it more technically intractable by prompting policy-makers to eschew the simplest, most effective policy remedies. Before laying out my argument in full, I must clarify how I understand three core concepts – health inequalities, welfare regimes, and neoliberalism – that are necessary background for the argument, but that may have different resonances for different audiences.