Rather than matching buyers and sellers order by order, an AMM prices assets algorithmically against a shared reserve of tokens, letting anyone trade instantly as long as the pool holds enough liquidity. This design replaced the order-book model borrowed from traditional finance with pure code, so trades settle against a formula instead of waiting for a counterparty to appear.

The original and still most common version, popularized by Uniswap, uses the constant product formula x*y=k: the two token reserves in a pool must always multiply to the same constant, so buying one asset automatically raises its price relative to the other. This creates a predictable curve, but it also means large trades relative to pool size move the price more, an effect called slippage. Depositors who fund these pools, known as liquidity providers, earn a share of trading fees in return, though they also face impermanent loss when the pooled tokens' prices diverge from each other.

Later designs refined the basic model. Curve's formula suits stablecoin pairs with minimal price movement, while Uniswap v3 and v4 let providers concentrate liquidity within chosen price ranges rather than spreading it across all possible prices, improving capital efficiency. Uniswap v4 further added customizable "hooks" that let developers attach extra logic, such as dynamic fees, to a pool.

AMMs underpin most of DeFi's swapping activity today, from PancakeSwap on BNB Chain to Curve and Balancer on Ethereum, because they need no centralized operator and let anyone become a market maker simply by depositing tokens.