This critical literature review synthesizes fragmented evidence on (GAI), sustainable supplier selection, and smart supply-chain optimization. Its purpose is to distinguish empirically demonstrated outcomes from conceptual claims and to identify conditions under which GAI can credibly support sustainable procurement. A thematic synthesis was organized around eight dimensions: ISC and digital integration; data quality and collaboration; forecasting and optimization; resilience, risk, and security; sustainability, carbon, ESG, and life-cycle assessment; circularity and reuse; adoption, readiness, and governance; and GAI, retrieval-augmented generation (RAG), explainable AI, and digital twins. Studies were appraised according to construct validity. A critical gap is the absence of controlled, supplier-level evaluations of end-to-end GAI systems that retrieve verifiable evidence, assess multi-dimensional sustainability criteria, explain recommendations, and track post-award performance. The review contributes a methodological bridge connecting AI capabilities, circularity, resilience, and adoption to a falsifiable research agenda for sustainable SCM.