Recent breakthroughs in machine learning (ML) technology are shifting the boundaries of what is technologically possible in several areas of Computer Science and Engineering. This paper discusses ML in the context of test-related activities, including fault diagnosis, post-silicon validation and yield optimization. ML is by now an established scientific discipline, and a large number of successful ML techniques have been developed over the years. This paper focuses on how to adapt ML approaches that were originally developed with other applications in mind to test-related problems. We consider two specific applications of learning in more depth: delay fault diagnosis in three-dimensional integrated circuits and tuning performed during post-silicon validation. Moreover, we examine the emerging concept of braininspired hyperdimensional computing (HDC) and its potential for addressing test and reliability questions. Finally, we show how to integrate ML into actual industrial test and yield-optimization flows.