The goal of this study is to explore and analyze the progress, methodologies, and maturity level of the composite materials Supply Chain (SC) from a sustainability lens. The SCOPUS database has been used to analyze the existing literature on composite materials SC, and VOS viewer software and MS Excel are used to analyze the data. First, a bibliometric analysis (Co-authorship of countries, Co-authorship analysis of authors, Co-occurrence analysis of keywords, and Bibliographic coupling of documents) has been carried out while following the PRISMA framework to explore and depict the overall growth of this research field. Second, an in-depth review of the selected papers (n = 20) addresses the concrete research questions for future research studies to build a bridge between the research gaps and the efforts to ensure a sustainable SC for composite materials. The outcomes of this research work reveal that the SC of composite materials is right now in its infant phase, which is not a saturated research field yet, and that much more research studies are required to add value to the existing knowledge of this field.