As an integral part of the decentralized finance (DeFi) ecosystem, decentralized exchanges (DEXs) with automated market maker (AMM) protocols have gained massive traction with the recently revived interest in blockchain and distributed ledger technology (DLT) in general. Instead of matching the buy and sell sides, automated market makers (AMMs) employ a peer-to-pool method and determine asset price algorithmically through a so-called conservation function. To facilitate the improvement and development of AMM-based decentralized exchanges (DEXs), we create the first systematization of knowledge in this area. We first establish a general AMM framework describing the economics and formalizing the system’s state-space representation. We then employ our framework to systematically compare the top AMM protocols’ mechanics, illustrating their conservation functions, as well as slippage and divergence loss functions. We further discuss security and privacy concerns, how they are enabled by AMM-based DEXs’ inherent properties, and explore mitigating solutions. Finally, we conduct a comprehensive literature review on related work covering both DeFi and conventional market microstructure.