Converter-based generators are increasingly replacing classical synchronous generation, resulting in significant challenges to the operation and planning of modern power systems. Power electronics (PE)-based equipment, along with non-linear PE-driven loads, introduce time-varying characteristics and fast switching behavior that increases the complexity of the power system model. Faster control actions are needed to overcome the fast switching dynamics to ensure the reliability and stability of future power systems. Thus, this requires advanced and detailed simulation methods and tools with highly accurate equivalent models to embody the relatively slower electromechanical to faster electromagnetic transient (EMT) phenomena. Conventional transient stability analysis using positive-sequence simulators has become inadequate for representing converter-dominated power systems, while EMT simulators suffer from the high computational burden. This review paper presents accelerated EMT simulation methods and tools that are categorized and discussed in three topics: system equivalents, simulation methods, and accelerating tools. Dynamic system equivalent techniques are discussed to model small to large interconnected external systems of the grid network. Moreover, a systematic review is made for existing EMT simulation methods, along with advanced co-simulation methods, for addressing simulation speed and accuracy issues in large power system networks. Emerging hardware-based simulation tools are reviewed that reduce the computational burden and increase the simulation efficiency of the power system model. Challenges and trends in EMT simulation are also presented and concluded by providing perspectives on this research topic. Review of Methods to Accelerate Electromagnetic Transient Simulation of Power Systems