Explore the adoption of blockchain-based decentralized exchanges in this 56-minute virtual talk from the SIAM Activity Group on Financial Mathematics and Engineering series. Delve into the market microstructure of Automated Market Makers (AMMs) and their fundamental differences from centralized limit order books. Examine a dynamic game theoretical model demonstrating how arbitrageurs extract gains from liquidity providers in decentralized finance (DeFi) applications. Investigate the impact of pricing curve convexity on price impact, arbitrage, liquidity freezes, and trading volume. Gain insights from transaction-level data analysis of Uniswap and SushiSwap AMMs. Cover topics including first-generation blockchain payment systems, liquidity provision, key DEX characteristics, model setup, and socially optimal curves. Understand the implications of this research for the rapidly evolving DeFi landscape, which currently manages over $57 billion USD.