The modular multilevel converter (MMC) is currently one of the power converter topologies which has attracted more research and development worldwide. Its features, such as high quality of voltages and currents, high modularity and high voltage rating, have made the MMC a very good option for several applications including high-voltage dc (HVdc) transmission, static compensators (STATCOMs), and motor drives. However, its unique features such as the large number of submodules, floating capacitor voltages, and circulating currents require a dedicated control system able to manage the terminal variables, as well as the internal variables with high dynamical performance. In this paper, a review of the research and development achieved during the last years on MMCs is shown, focusing on the challenges and proposed solutions for this power converter still faces in terms of modeling, control, reliability, power topologies, and new applications.