With the global trend of pursuing clean energy and decarbonization, power systems have been evolving in a fast pace that we have never seen in the history of electrification. This evolution makes the power system more dynamic and more distributed, with higher uncertainty. These new power system behaviors bring significant challenges in power system modeling and simulation as more data need to be analyzed for larger systems and more complex models to be solved in a shorter time period. The conventional computing approaches will not be sufficient for future power systems. This paper provides a historical review of computing for power system operation and planning, discusses technology advancements in high performance computing (HPC), and describes the drivers for employing HPC techniques. Some high performance computing application examples with different HPC techniques, including the latest quantum computing, are also presented to show how HPC techniques can help us be well prepared to meet the requirements of power system computing in a clean energy future.