Persistent data structures are data structures that preserve their previous versions when they are modified. This means that instead of overwriting data, they create a new version while keeping the old version intact. This feature is particularly useful in functional programming, where immutability is a core principle. These structures allow for efficient access to historical data, enabling operations like undoing changes or accessing past states without duplicating the entire structure. Common examples include persistent lists, trees, and maps, which can be implemented in various programming languages to enhance performance and maintainability.