This paper presents a detailed description of Finite Control Set Model Predictive Control (FCS-MPC) applied to power converters. Several key aspects related to this methodology are in depth presented and compared with traditional power converter control techniques, such as linear controllers with PWM based modulation methods. The basic concepts, operating principles, control diagrams and results are used to provide a comparison between the different control strategies. The analysis is performed on a traditional three-phase voltage source inverter, used as simple and comprehensive reference frame. However, additional topologies and power systems are addressed to highlight differences, potentialities and challenges of FCS-MPC. Among the conclusions are the feasibility and great potential of FCSMPC due to today's signal processing capability, specially for power systems with a reduced number of switching states and more complex operating principles, such as matrix converters. In addition, the possibility to address different or additional control objectives easily in a single cost function, enables a simple, flexible and improved performance controller for power conversion systems.