Large language models (LLMs) have sparked significant impact with regard to both intelligence and productivity. Numerous enterprises have integrated LLMs into their applications to solve their own domain-specific tasks. However, integrating LLMs into specific scenarios is a systematic process that involves substantial components, which are collectively referred to as the LLM supply chain. A comprehensive understanding of LLM supply chain composition, as well as the relationships among its components, is crucial for enabling effective mitigation measures for different related risks. While existing literature has explored various risks associated with LLMs, there remains a notable gap in systematically characterizing the LLM supply chain from the dual perspectives of contributors and consumers. In this work, we develop a structured taxonomy encompassing risk types, risky actions, and corresponding mitigations across different stakeholders and components of the supply chain. We believe that a thorough review of the LLM supply chain composition, along with its inherent risks and mitigation measures, would be valuable for industry practitioners to avoid potential damages and losses, and enlightening for academic researchers to rethink existing approaches and explore new avenues of research.