In this article, the notion of reinsurance as a means for a first-line insurer to pass on part of his underwritten risk for some appropriate premium payment is defined and motivated. Various forms of common reinsurance treaties of proportional and nonproportional types are described, including quota-share, surplus, excess-of-loss, stop-loss, and large-claim treaties. Some actuarial and practical challenges in connection with the determination of suitable premiums for the reinsured risk are discussed. Subsequently, main obstacles in deciding upon the choice of the appropriate reinsurance form in a given situation are treated, which often can be expressed as an optimization problem with an objective function under constraints. Finally, connections between reinsurance and the realm of finance are discussed. Throughout the article, references to the literature and links to other articles are provided.