The Modular Multilevel Converter (MMC), even though a fairly recent converter, is considered a very important one for the future of electrical power systems, variable speed drives and other applications. The MMC enables ac-dc and dc-ac conversion at virtually any voltage levels without relying on bulky transformers. This work presents a newly developed comprehensive control oriented model and a control strategy implementation that focuses on rectifier applications for medium voltage drives and is naturally derived from the presented model. In addition, a survey on existing MMC control strategies is presented.