This article aims at presenting the current structure of the Brazilian National Graduate Program. It describes the development of the courses from their starting point in the Thirties focusing on the last six decades. It demonstrates that after the country set up the two national agencies to foster science and technology, CAPES and CNPq, investments in this area have increased tremendously. As a result the number of courses and the numbers of Master's and doctoral enrollments have soared. The current Brazilian National Graduate Program is presented in full. Moreover, while scientific production has also increased, technological development and innovation are still lacking pace. The role played by state agencies for research development is emphasized as an important additional way of complementing the federal agencies. Despite the advancement made, the article points out important challenges that are still to be faced to put Brazil in a better position in international scientific rankings.