Uniswap exchange uses a "Market Maker" mechanism, where liquidity providers store a reserve of ETH and ERC20 tokens within an Ethereum smart contract. An exchange rate is set between the tokens and ETH based on the relative availibility of each token. Arbitrage ensures that the rate will be the same as on other exchanges. Buyers who send Token 1 to the smart contract will receive back Token 2 at the current rate. A small fee is paid from the buyer to the liquidity providers to incentive participation.
A full writeup with math and whatnot will be written soon. Until then, here is some more info on Market Makers:
https://www.reddit.com/r/ethereum/comments/55m04x/lets_run_onchain_decentralized_exchanges_the_way/ http://vitalik.ca/general/2017/06/22/marketmakers.html
Please reach out if you would like to get involved or support the project.
Demo: https://uniswap.io/ Email: hayden@uniswap.io ETH Address: 0x4779721CaC18A46DbCF148f2Dd7A8E6cc1F90078