In the era of globalization, industries of critical metals are organized through the global supply chain. However, the global supply chains have been disrupted since 2020 by the outbreak of COVID-19 and a series of geopolitical crises. To better address the supply chain challenges of critical metals, a review is needed about the sources, propagation, and responses of the supply chain risks. Firstly, this review provides an overview about the research progress in identifying the risk sources and assessing the risks and then proposes a new supply chain framework, categorizing relevant risk factors into upstream risks, middle-stream risks, downstream risks, and general risks, for risk analysis of critical metals. Secondly, this review offers a comprehensive understanding about how the risks propagate horizontally and vertically. Finally, responses such as supply diversification, stockpiling, material substitution, recycling and circular economy strategy, price volatility hedging, and supply chain traceability are reviewed. This survey features the supply chain perspective, overviews on network-based studies, and affirms the urgency and need for further studies on supply chain risks and resilience, which may contribute to a smooth clean energy transition.