Modular multilevel converters (MMC) are gradually becoming the technology of choice in high-voltage direct current (HVDC) power transmission for grid integration of large-scale offshore wind farms and multi-terminal HVDC transmission schemes. Each phase of an MMC HVDC terminal consists of several hundreds of identical submodules that switch a module capacitor in and out of the circuit to synthesize near perfect sinusoidal ac voltages. This operation requires sophisticated control and modulation techniques. Furthermore, the design of converter, validation of control system and operational planning requires robust simulation models. To precisely model the switching operation in the converters electromagnetic transient solvers are employed. These solvers utilize numerical integration methods and nodal analysis to resolve the system in time domain. However, the design of MMC poses a computational challenge to the classical electromagnetic transient simulations techniques. Independent operation of submodules necessitates explicit their modeling, which leads to hundreds of nodes and semiconductor devices in the equivalent models. This time-varying topology with hundreds of nodes leads to the excessive computational load on the electromagnetic transient solvers. To address this, existing literature proposes numerous efficient equivalent models for MMC based on submodule/arm's Thevenin's equivalence, switching function or average representations. The desired equivalent models for EMT studies are expected to reproduce internal and external dynamics of the converter in stationary and transient conditions. However, many of the existing models in literature lack the capability to capture the blocked state of operation of submodules, which finds application in the dc fault operation of the converter. Furthermore, with an extensive collection of proposed models, existing literature lacks an independent collective objective comparison of proposed models, which enable suitable selection of model based on the simulation needs. In light of these requirements, this thesis presents a comprehensive review and enhances models from the existing literature. Moreover, using PSCAD/EMTDC simulations the proposed models are evaluated against the detailed model of the converter regarding accuracy and computational load. The simulations confirm the ability of enhanced models to capture the dynamics of converter under stationary and severe transient conditions. Furthermore, based on the simulation methods and results, the thesis addresses limitations of the proposed models and presents recommendations for their simulation applications. In addition to the specific focus on electromagnetic transient simulation models, the thesis further aims to serve as a tutorial for the MMCs technology. Therefore the thesis presents a detailed account of MMC operation, and its associated control and modulation system.