Integral quadratic constraints (IQC*) are inequalities used to describe (partially) possible signal combinations within a given dynamical system. IQC offer a framework for abstracting “challenging” (e.g., nonlinear, time-varying, uncertain, or distributed) elements of dynamical system models to aid in rigorous analysis of robust stability and performance (more specifically, to establish L2 gain bounds, passivity, and other system properties, which can be expressed, exactly or approximately, in terms of generalized dissipativity). While the technique can be employed to prove general theorems, it is most powerful when used to derive optimization-based algorithms for certification of stability and robustness of specific feedback systems.