The main objective of this paper is to explore the opening of the reinsurance market in Brazil, its peculiarities and importance. In order to contribute to a better understanding of this process, we highlight the main technical foundations of reinsurance, the importance of its use for solvency and stabilization of results of insurance companies and the evolution of the opening of the market, as well as its current composition. The technical foundations of reinsurance were explained concisely in order to improve understanding for the application of the theory concerning the process of breaking the monopoly of the Brazilian reinsurance market.