Party polarization—or the degree to which political parties disagree ideologically—is now multidimensional in most European democracies. Continuing to rely on a single left-right dimension risks obscuring an increasingly complex and fragmented political landscape. But what are the consequences of multidimensional polarization for the functioning of democracy? This project seeks to answer that question by [1] mapping multidimensional polarization among political parties across Europe (1970–present), and analyzing its consequences for [2] political engagement (e.g., voter turnout) and [3] partisan hostility. It will do so using a combination of innovative statistical methods, observational analyses, and experimental research designs.