This article describes the optimization models recently applied to the design and operation of power systems towards forming smart grids and identifies trends, barriers, and possible gaps in this area. Models are described to optimize the design and operation of power systems considering renewable energies, distributed generation, microgrids, demand management, and energy storage systems. It was concluded that it is necessary to validate many of the models formulated recently to optimize the operation through tests with real data and on a large scale. Furthermore, demand management and microgrids are aspects in which it is necessary to develop models for optimal power flow. Finally, it is necessary to predict stochastic variables with greater precision so that these models adapt to the real behavior of the system.