The long-run U-shaped patterns of economic inequality are standardly explained by basic economic trends (Piketty's r>g), taxation policies, or 'great levelers,' like catastrophes. This paper argues that housing policy, in particular rent control, is a neglected explanatory factor in understanding overall inequality. We hypothesize that rent control could decrease overall housing wealth, lower incomes of generally richer landlords, and increase disposable incomes of generally poorer tenants. Using original long-run data for up to 16 countries (1900-2016), we show that rent controls lowered wealth-to-income ratios, top income shares, Gini-coefficients, rent increases, and rental expenditure. A counterfactual analysis using micro-data from the Luxembourg Income Study shows that rent controls could reduce rental expenditure of mostly lower-income tenants and rental incomes of mostly higher-income landlords. Overall, rent controls must be strict in order to have tangible effects and, historically, only strict rent controls have significantly reduced inequalities. The paper argues that housing policies should generally receive more attention in understanding economic inequalities.