What are the benefits of a DEX?

Can you elaborate on the advantages of using a Decentralized Exchange (DEX) over a traditional, centralized cryptocurrency exchange? Are there any specific benefits that users can expect when trading on a DEX platform, such as increased security, anonymity, or greater control over their funds? Additionally, how does the decentralized nature of a DEX impact trading fees and liquidity? I'm interested in understanding the full scope of benefits that come with using a DEX for cryptocurrency trading.