The paper starts with a brief account of the origins of MPD concept followed by an explanation of Lorentz force. The nature of an ideal Self-field MPD thruster is then discussed in terms of basic thrust law, cubic dependance and ideal scaling trends. The situation as to real Self-field MPD thrusters follows including their electrical characteristics, deviations from the ideal, the Hall and back-EMF effect and the role of Alfvén's critical ionization velocity. Onset phenomenology and the critical onset parameter are then discussed. The main theories proposed to explain the onset phenomena are summarized, such as mass starvation, instabilities, back EMF and macroscopic instabilities. A summary of onset follows with a discussion of attempts made to prevent onset. Applied field MPD thrusters are then presented, followed by Lithium propellant devices. A survey of major R&D efforts on MPD thrusters worldwide is made. Finally, some concluding remarks are made as to the status and prospects of MPD propulsion.