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This review systematically examines the handling—or more often the neglect—of domain shift within the materials machine learning literature published between 2017 and 2023, drawing on a targeted search of peer-reviewed publications across specialized databases and journals to compile and analyze exactly 30 representative studies that span foundational overviews, application-focused works, and methodological explorations. Domain shift in materials science takes four distinct yet interrelated forms—temporal, compositional, experimental, and theoretical—each arising from the inherently heterogeneous nature of materials data sources that range from evolving laboratory protocols and diverse chemical families to inter-laboratory variations and discrepancies between computational approximations and experimental realities. Current practices reveal that explicit acknowledgment of domain shift remains rare, with the majority of papers proceeding under the default assumption of identical training and test distributions. At the same time, detection methods and adaptation strategies appear in fewer than one in five studies, leaving models vulnerable to silent degradation when deployed on real-world materials problems. The surveyed methods for handling domain shift include statistical detection techniques, domain-adversarial training frameworks, feature-alignment approaches, and shift-robust evaluation protocols, many of which have been proposed in adjacent machine-learning fields yet remain underutilized in materials contexts despite their direct relevance to property prediction and inverse design tasks. Collectively, these findings underscore the urgent need for standardized shift-reporting protocols, the development of materials-specific out-of-distribution benchmarks, and the integration of domain-adaptation pipelines into routine workflows, thereby elevating the reliability, generalizability, and practical utility of machine-learning models in accelerating materials discovery.