We put forth a framework for expressing security requirements from interactive protocols in the presence of arbitrary leakage. The framework allows capturing different levels of leakage-tolerance of protocols, namely the preservation (or degradation) of security, under coordinated attacks that include various forms of leakage from the secret states of participating components. The framework extends the universally composable (UC) security framework. We also prove a variant of the UC theorem that enables modular design and analysis of protocols even in face of general, non-modular leakage. We then construct leakage-tolerant protocols for basic tasks, such as secure message transmission, message authentication, commitment, oblivious transfer and zero-knowledge. A central component in several of our constructions is the observation that resilience to adaptive party corruptions (in some strong sense) implies leakage-tolerance in an essentially optimal way.