Several advanced economies implemented negative nominal interest rates in the middle of the last decade, seeking to provide further monetary accommodation once cuts in positive territory had been exhausted. Negative rates affect banks in novel ways, mostly because during times of negative policy rates the interest rate that banks pay households on their deposits usually remains close to zero. In this review, we analyze the large literature that studies the impact of negative nominal interest rates, proceeding in four steps. First, we explain the theoretical channels through which negative rates affect banks. Second, we discuss the empirical findings about bank outcomes under negative rates. Third, we describe the aggregate transmission channels that influence the macroeconomic implications of a policy rate cut in negative territory. Finally, we compare the general-equilibrium models that have been used to quantify the effectiveness of negative rates and highlight why they have obtained mixed results. We conclude that, if properly implemented, negative rates are a valuable tool that central banks should not discard outright. However, negative rates can have quantifiable costs for the financial sector, and their effectiveness is likely to decline if implemented for long periods.