Real-time simulation enables the understanding of system operating conditions by evaluating simulation models of physical components running synchronized at the real-time wall clock. Leveraging the real-time measurements of comprehensive system models, faster than real-time (FTRT) simulation allows the evaluation of system architectures at speeds faster than real-time. FTRT simulation can assist in predicting the system's behavior efficiently, thus assisting the operation of system processes. Namely, the provided acceleration can be used for improving system scheduling, assessing system vulnerabilities, and predicting system disruptions in real-time systems. The acceleration of simulation times can be achieved by utilizing digital real-time simulators (RTS) and high-performance computing (HPC) architectures. FTRT simulation has been widely used, among others, for the operation, design, and investigation of power system events, building emergency management plans, wildfire prediction, etc. In this paper, we review the existing literature on FTRT simulation and its applications in different disciplines, with a particular focus on power systems. We present existing system modeling approaches, simulation tools and computing frameworks, and stress the importance of FTRT accuracy.