Lending pools are decentralized applications which allow mutually untrusted users to lend and borrow crypto-assets. These applications feature complex, highly parametric incentive mechanisms to equilibrate the loan market. This complexity makes the behaviour of lending pools difficult to understand and to predict: indeed, ineffective incentives and attacks could potentially lead to emergent unwanted behaviours. Reasoning about lending pools is made even harder by the lack of executable models of their behaviour: to precisely understand how users interact with lending pools, eventually one has to inspect their implementations, where the incentive mechanisms are intertwined with low-level implementation details. Further, the variety of existing implementations makes it difficult to distill the common aspects of lending pools. We systematize the existing knowledge about lending pools, leveraging a new formal model of interactions with users, which reflects the archetypal features of mainstream implementations. This enables us to prove some general properties of lending pools, such as the correct handling of funds, and to precisely describe vulnerabilities and attacks. We also discuss the role of lending pools in the broader context of decentralized finance.