This paper summarises the academic literature on the financial market pricing of physical and transition risks related to climate change. While studies find that these risks are starting to be priced, concerns are growing that current prices do not fully reflect the risks. Investors grapple with three major challenges when seeking to price climate risks adequately. First, the aggregate nature of climate risks limits the availability of risk-sharing arrangements and hedging instruments. Second, the high degree of uncertainty about climate risks and concrete policy actions to address them heightens modelling and measurement challenges. Third, the information available to investors about climate risks and their consequences is often incomplete or imperfect.