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Domain adaptation has emerged as a promising strategy for cross-composition materials prediction, where models trained on one compositional regime are transferred to chemically distinct but related target domains. This review examines the literature from 2017 to 2024 on domain adaptation in materials informatics, with a specific focus on prediction tasks spanning binary, ternary, quaternary, and high-entropy systems. It argues that although transfer-based methods are increasingly used to reduce dependence on expensive first-principles calculations and scarce experimental measurements, their application often rests on theoretical assumptions that remain untested in materials contexts. Across the reviewed studies, six recurrent assumptions are identified: shared feature space, covariate shift only, sufficient source–target overlap, label-function stability, sample independence, and availability of target-domain data. The review shows that these assumptions are fragile under composition-induced shifts, where new bonding environments, structural prototypes, and electronic behaviors frequently alter the underlying prediction problem. It further synthesizes the field into six methodological categories—feature alignment, adversarial adaptation, reweighting, fine-tuning, multi-source adaptation, and unsupervised adaptation—and evaluates their strengths, vulnerabilities, and suitability under varying similarity regimes. Five core trade-offs structure current practice, particularly those involving performance versus negative transfer, simplicity versus flexibility, and theory versus empirical reliability. The review also identifies persistent gaps, including the lack of standardized benchmarks, weak similarity quantification, limited reporting of failure cases, and insufficient evaluation under true extrapolation. In response, it proposes a validation and reporting framework centered on pre-adaptation diagnostics, explicit similarity scoring, comparative baselines, negative-transfer reporting, and computational transparency. Overall, the review concludes that domain adaptation is most reliable as a data-efficiency tool within compositionally similar neighborhoods, but remains brittle and potentially misleading when applied across chemically distant domains without diagnostic validation.