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The integration between blockchain and artificial intelligence (AI) has gained a lot of attention in recent years, especially since such integration can improve security, efficiency, and productivity of applications in business environments characterised by volatility, uncertainty, complexity, and ambiguity. In particular, supply chain is one of the areas that have been shown to benefit tremendously from blockchain and AI, by enhancing information and process resilience, enabling faster and more cost-efficient delivery of products, and augmenting products’ traceability, among others. This paper performs a state-of-the-art review of blockchain and AI in the field of supply chains. More specifically, we sought to answer the following three principal questions: Q1—What are the current studies on the integration of blockchain and AI in supply chain?, Q2—What are the current blockchain and AI use cases in supply chain?, and Q3—What are the potential research directions for future studies involving the integration of blockchain and AI? The analysis performed in this paper has identified relevant research studies that have contributed both conceptually and empirically to the expansion and accumulation of intellectual wealth in the supply chain discipline through the integration of blockchain and AI.