In this chapter, we provide an overview of the reinsurance market, including an analysis of the factors driving the demand for reinsurance, and of the impact of climate change. We further discuss moral hazard issues and challenges faced by the reinsurance industry. We present a number of tools, coming from the insurance literature that are available to model reinsurance and alternative risk transfers, but we also show that more research is needed to capture the specifics of these markets. In particular, the lack of financial market dynamics into actuarial pricing models is highlighted as one important limit of the surveyed models.