How do decentralized exchanges work behind the scenes, and what role do smart contracts play in them?

I’ve always been fascinated by decentralized exchanges but never really understood how they work behind the scenes. While researching, I found https://merehead.com/blog/make-decentralized-exchange-script/, and it broke everything down in a way that finally made sense to me. The part about smart contract integration was particularly interesting. Now, I’m thinking about testing a few open-source scripts just to see how they function in a real-world setting.