We discuss political economy mechanisms which can explain the resource curse, in which an increase in the size of resource rents causes a decrease in the economy's total value added. We identify a number of channels through which resource rents will alter the incentives of a political leader. Some of these induce greater investment by the leader in assets that favour growth (infrastructure, rule of law, etc.), others lead to a potentially catastrophic drop in such activities. As a result, the effect of resource abundance can be highly non-monotonic. We argue that it is critical to understand how resources affect the leader's 'survival function', i.e. the reduced-form probability of retaining power. We also briefly survey decentralized mechanisms, in which rents induce a reallocation of labour by private agents, crowding out productive activity more than proportionately. We argue that these mechanisms cannot be fully understood without simultaneously studying leader behaviour.