A group of minerals has emerged in recent years as critical to low-carbon energy and other technologies. The extraction and processing of these minerals will have to increase substantially if countries’ plans for transitioning away from fossil fuels are to be realised. This paper sets out the challenges posed by this projected expansion in mineral production, and how they need to be addressed if this expansion is to take place. One of the main challenges is the mobilisation of the necessary level of investment in the production of these minerals, which involves specific risks beyond the inherent risks of exploration and mine development, including uncertainty about future technological trajectories, the potential for conflict with host communities, the concentration of mineral processing in China, and extended and vulnerable supply chains. Risks of conflict can be reduced by ‘responsible mining’ that gives enhanced attention to the environmental, social and governance (ESG) issues raised by mining, and supply chains can be made more resilient, and the need for new mines reduced, by implementing circular economy strategies to keep mineral products in use for as long as possible. ‘Sustainable finance’ is an approach to investment with such considerations at its heart, but which may need a ‘green premium’ to be widely implemented. The paper explores all these issues in detail and ends with a series of recommendations for how the production of energy transition and other critical minerals can be secured at the required level in a sustainable and responsible way in the future.