This talk considers the use of Integral Quadratic Constraints (IQCs) for stability and performance analysis. IQC analysis theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. This talk focuses on the time-domain, dissipation inequality perspective. First, the time-domain approach to IQCs is reviewed along with the associated numerical algorithms to perform the analysis. Next, the connections between the frequency domain and time-domain approaches are clarified. Finally, several extensions enabled by the time-domain approach are provided, e.g. to nonlinear and time-varying systems.