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This tutorial paper describes novel scalable, non-linear/generic, and industrially-oriented approaches to perform variation-aware modeling, verification, fault simulation, and testing of analog/custom ICs. In the first section, Dimitri De Jonghe, Elie Maricau, and Georges Gielen present a new advance in extracting highly nonlinear, variation-aware behavioral models, through the use of data mining and a re-framing of the model-order reduction problem. In the next section, Trent McConaghy describes new statistical machine learning techniques that enable new classes of industrial EDA tools, which in turn are enabling designers to perform fast and accurate PVT/statistical/high-sigma design and verification. In the third section, Bratislav Tasić presents a novel industrially-oriented approach to analog fault simulation that also has applicability to variation-aware design. In the final section, Haralampos Stratigopoulos describes describes state-of-the-art analog testing approaches that address process variability.