We propose a theory of indebted demand, capturing the idea that large debt burdens by households and governments lower aggregate demand, and thus natural interest rates. At the core of the theory is the simple yet under-appreciated observation that borrowers and savers differ in their marginal propensities to save out of permanent income. Embedding this insight in a two-agent overlapping-generations model, we find that recent trends in income inequality and financial liberalization lead to indebted household demand, pushing down natural interest rates. Moreover, popular expansionary policies—such as accommodative monetary policy and deficit spending—generate a debt-financed short-run boom at the expense of indebted demand in the future. When demand is sufficiently indebted, the economy gets stuck in a debt-driven liquidity trap, or debt trap. Escaping a debt trap requires consideration of less standard macroeconomic policies, such as those focused on redistribution or those reducing the structural sources of high inequality.