The talk will present recent work dealing with the introduction of a notion of reversibility in concurrent languages. Reversibility refers to the ability to undo an execution and to revert it to a prior state. Such a facility can be useful for a variety of purposes, including debugging, safe exception handling, programming atomic operations and transactions, and more generally programming recoverable systems. The talk will discuss how to introduce reversibility in a paradigmatic concurrent language, the higher-order pi-calculus, and will discuss the subtleties involved in defining a semantically sound rollback primitive.