This survey provides a comprehensive analysis on recent research related to optimization and simulation in the new paradigm of power systems, which embraces the so-called smart grid. We start by providing an overview of the recent research related to smart grid optimization. From the variety of challenges that arise in a smart grid context, we analyze with a significance importance the energy resource management problem since it is seen as one of the most complex and challenging in recent research. The survey also provides a discussion on the application of computational intelligence, with a strong emphasis on evolutionary computation techniques, to solve complex problems where traditional approaches usually fail. The last part of this survey is devoted to research on large-scale simulation towards applications in electricity markets and smart grids. The survey concludes that the study of the integration of distributed renewable generation, demand response, electric vehicles, or even aggregators in the electricity market is still very poor. Besides, adequate models and tools to address uncertainty in energy scheduling solutions are crucial to deal with new resources such as electric vehicles or renewable generation. Computational intelligence can provide a significant advantage over traditional tools to address these complex problems. In addition, supercomputers or parallelism opens a window to refine the application of these new techniques. However, such technologies and approaches still need to mature to be the preferred choice in the power systems field. In summary, this survey provides a full perspective on the evolution and complexity of power systems as well as advanced computational tools, such as computational intelligence and simulation, while motivating new research avenues to cover gaps that need to be addressed in the coming years.