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.
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.
Meet the people behind these projects Youtube - Token Summit II - Understanding Decentralized Exchange dec 2017