Cross-chain exchanges operate by enabling interoperability between different blockchains, allowing users to trade assets from one blockchain for assets from another directly. This is achieved through various mechanisms, such as atomic swaps, wrapped tokens, or utilizing decentralized protocols that facilitate such exchanges. The technology aims to enhance liquidity in the cryptocurrency market by providing traders with access to assets on multiple blockchains without needing to first transfer to a centralized exchange. Users maintain control over their keys and assets, promoting decentralization and security.