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High-test quality plays a central role in the development of successful products used for building robust computing and communication systems. Hence, high-test quality enablers are rapidly becoming "features", just like performance, power-consumption and die size. This tutorial includes in-depth discussions on two major test topics that are essential for designs manufactured in nanometer technologies: test compression and diagnosis. Test compression techniques enable orders of magnitude improvement (reduction) in test cost and pave the path for successful implementation of built-in-self-test features. Ensuring products yield with sufficient quality also requires techniques for identifying and characterizing defects. This tutorial describes state-of-the-art techniques for performing defect diagnosis and how such techniques are key in enabling high-yielding and high-quality products. Supporting data from actual designs and manufacturing processes are presented.