Robert C. Merton's contributions are current. Regarding the design of retirement plans, in a framework of pension deficient systems, the investigations of Merton (1969) and (1971) on optimal consumption and portfolio rules during and after working life acquire contemporary validity. Likewise, Bodie and Merton (2002) propose the use of derivative products, at the international level, to diversify the risks of pension systems just at the moment when these systems of many underdeveloped and industrialized economies are on the verge of collapse; knowing that several of these systems only provide a meager proportion of the salary. Finally, Merton's theory of rational option pricing is retaken to create synthetic oil pipelines and power plants through the use of contingent claims. This paper aims to review the trends and perspectives in financial science and mathematical finance, within the framework of the pioneering contributions of Robert Cox Merton, highlighting priority areas that offer opportunities for research with social and global impacts.