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The rapidly growing interest in machine learning (ML) for materials discovery has resulted in a large body of published work. However, only a small fraction of these publications includes confirmation of ML predictions, either via experiment or via physics-based simulations. In this review, we first identify the core components common to materials informatics discovery pipelines, such as training data, choice of ML algorithm, and measurement of model performance. Then we discuss some prominent examples of validated ML-driven materials discovery across a wide variety of materials classes, with special attention to methodological considerations and advances. Across these case studies, we identify several common themes, such as the use of domain knowledge to inform ML models.