The past two decades have witnessed widespread attempts to reform fossil fuel subsidies in developing countries. If the reforms are likely to improve economic efficiency, the expected effects on income distribution and poverty are more controversial. This paper reviews the recent literature that examines the impacts of fossil fuel subsidies and their reform on income inequality and poverty. It identifies the different channels that have been explored in the literature and surveys the empirical evidence on the importance of these channels in practice. Drawing on diverse country experiences, it also discusses why fossil fuel subsidies are particularly challenging to reform and highlights several ways in which efforts to reform may be feasible and successful.