Over the past decade, modular multilevel converters have evolved as the preferred choice for high voltage conversion systems. The design of the converter poses a computational challenge to the classical electromagnetic transient simulation techniques, for which the existing literature proposes numerous simplified and computationally-efficient equivalent representations. Despite the extensive collection of proposed models, the literature lacks a systematic comparison of these representations, which could enable their appropriate selection based on the specific simulation objectives. In light of these requirements, this article presents a comprehensive review of MMC models and discusses their applicability for parallel and real-time simulation. Using PSCAD/EMTDC simulations, the models are objectively compared with regards to computational efficiency and accuracy for various transient conditions. In addition, the paper also presents a brief account of MMC operation and the associated control and modulation system.