This paper presents a review of a beamed energy propulsion rocket, the Microwave Rocket, which produces propulsive thrust from millimeter-wave beams transferred from the ground. The thrust is generated through millimeter-wave discharge driven in a cylindrical thruster. As a high-power millimeter-wave generator, a Gyrotron is promising as the beam source. The salient benefit of Microwave Rockets is the resultant drastic cost reduction of mass transportation into space. We have already conducted launch experiments and have achieved continuous thrust generation under multi-pulse operation. Recently, a long-distance beam transfer system has been developed. Ignition tests have been conducted. The physics of the millimeter-wave discharge remain unclear. Additional studies using experimentation and calculations must be conducted to optimize the thrust generation.