Research on cryptocurrency exchanges, consisting of both centralized exchanges (CEXs) and decentralized exchanges (DEXs), has seen a significant increase in contributions in recent years, driven by growing interest in the conceptual design of cryptocurrency markets. Through a comprehensive review of literature published between January 2019 and September 2023, I identify and analyze different dimensions of the ongoing CEX vs. DEX debate. While DEXs emphasize decentralization, user control, and resistance to censorship, CEXs offer higher liquidity, advanced trading features, and a more established track record. Regulatory challenges, such as Know Your Customer (KYC) and Anti-Money Laundering (AML) compliance, also feature prominently in the literature and influence the choice of exchange for both traders and policymakers. In addition, I observe a growing interest in the design of pricing functions for CEXs and DEXs, particularly in the area of automated market makers (AMMs). Finally, based on my findings, I outline future research opportunities in this context and derive research gaps as well as recommended actions for practitioners.
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