Decentralized exchanges
The goal of decentralized exchanges is to tackle the problem of the single point of failure, to improve transparency (on-chain exchanges) and improve security (users hold the keys to their wallets, not the exchange).
A stage intermediate between centralized and decentralized is semi-decentralized: exchange keeps order books on its server, but not the private keys.
For review, see
Decentralized Cryptocurrency Exchanges
State of Decentralized Exchanges, 2018
Decentralized exchanges promise lower transaction fees compared to the centralized ones since they do not require proprietary infrastructure. However, they will likely require much higher level of user tech savvy; hence centralized exchanges are likely to persist as onramping vehicles, allowing to convert fiat into crypto.
0x provides a settlement layer that is being used to build decentralized exchanges.
One early DEX is EtherDelta
BitShares 2.0 is also one of the earliest decentralised exchanges. A stable coin BitUSD was also introduced (quick look at the price shows no stability whatsoever???)
Meet the people behind these projects Youtube - Token Summit II - Understanding Decentralized Exchange dec 2017