In the 40 years after its introduction in 1947, the Simplex Method has strongly dominated the field of linear programming. Simultaneously, in the 1960s, nonlinear problems were considered intrinsically different from linear problems and were solved by means of a so-called logarithmic barrier method. Attention however turned to different methodologies for nonlinear problems due to strong concerns about the inherent ill conditioning of barrier methods. In 1984, Karmarkar started what was to become the interior-point revolution by introducing a polynomial algorithm for linear programming capable of outperforming the Simplex. His method was later shown to be formally equivalent to a logarithmic barrier method and its ill conditioning to be benign. Linear and nonlinear programs were unified. We review the evolution of interior-point methods for linear and nonlinear programming from the early days to present, focusing on the primal-dual formulation. We examine some of the most recent ideas developed, for the most part, in the past decade, and some of the most effective numerical implementations for modern large-scale problems.