© 2020 by the authors. Licensee MDPI, Basel, Switzerland.A modular multilevel converter (MMC) is an advanced voltage source converter applicable to a wide range of medium and high-voltage applications. It has competitive advantages such as quality output performance, high modularity, simple scalability, and low voltage and current rating demand for the power switches. Remarkable studies have been carried out regarding its topology, control, and operation. The main purpose of this review is to present the current state of the art of the MMC technology and to offer a better understanding of its operation and control for stationary applications. In this study, the MMC configuration is presented regarding its conventional and advanced submodule (SM) and overall topologies. The mathematical modeling, output voltage, and current control under different grid conditions, submodule balancing control, circulating current control, and modulation methods are discussed to provide the state of the MMC technology. The challenges linked to the MMC are associated with submodule balancing control, circulating current control, control complexity, and transient performance. Advanced nonlinear and predictable control strategies are expected to improve the MMC control and performance in comparison with conventional control methods. Finally, the power losses associated with the advanced wide bandgap (WBG) power devices (such as SiC, GaN) are explored by using different modulation schemes and switching frequencies. The results indicate that although the phase-shifted carrier-based pulse width modulation (PSC-PWM) has higher power losses, it outputs a better quality voltage with lower total harmonic distortion (THD) in comparison with phase-disposition pulse width modulation (PD-PWM) and sampled average modulation pulse width modulation (SAM-PWM). In addition, WBG switches such as silicon carbide (SiC) and gallium nitride (GaN) devices have lower power losses and higher efficiency, especially at high switching frequency in the MMC applications.