This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters, From an original idea by Yakubovich, the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC’s) for its elementary components, A stability theorem for systems described by IQC’s is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality, A systematic computational approach is described, and relations to other methods of stability analysis are discussed, Last, but not least, the paper contains a summarizing list of IQC’s for important types of system components.