How do dex swaps work?

Could you please explain in simple terms how decentralized exchange (DEX) swaps function? I'm particularly curious about the process behind the transactions, how users can trade cryptocurrencies peer-to-peer without a central authority, and the role of smart contracts in facilitating these swaps. Additionally, I'd like to know if there are any risks or limitations associated with using DEXs for swapping cryptocurrencies. Thank you for your assistance.