Recent advancements in decentralized finance (DeFi) have resulted in a rapid increase in the use of Automated Market Makers (AMMs) for creating decentralized exchanges (DEXs). In this paper, we organize these developments by treating an AMM as a neoclassical black-box characterized by the conversion of inputs (tokens) to outputs (prices). The conversion is governed by the technology of the AMM summarized by an ‘exchange function'. Various types of AMMs are examined, including: Constant Product Market Makers; Constant Mean Market Makers; Constant Sum Market Makers; Hybrid Function Market Makers; and, Dynamic Automated Market Makers. The paper also looks at the impact of introducing concentrated liquidity in an AMM. Overall, the framework presented here provides an intuitive geometric representation of how an AMM operates, and a clear delineation of the similarities and differences across the various types of AMMs.