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Schemes have been suggested for transferring energy from Earth-to-space, space-to-Earth, and space-to-space using high-power microwave (HPM) beams. All use power beaming. Microwave beams have been studied for propelling spacecraft for launch to orbit, orbit raising, launch from orbit into interplanetary and interstellar space, and deployment of large space structures. The microwave thermal rocket, called the ldquomicrowave thermal thruster,rdquo is a reusable single-stage vehicle that uses an HPM beam to provide power to a heat-exchanger propulsion system, with double the specific impulse of conventional rockets. Orbital missions include orbit raising and space solar power. Microwave-propelled sails are a new class of spacecraft that promises to revolutionize future space probes. Experiments and simulations have verified that sails riding beams can be stable on the beam for conical sail shapes. Beam-driven sail flights have now demonstrated the basic features of the beam-driven propulsion. Beams can also carry angular momentum and communicate it to a sail to help control it in flight. An early mission for microwave space propulsion is dramatically shortening the time needed for sails to escape Earth's orbit. A number of missions for beam-driven sails have been quantified for high-velocity mapping of the outer solar system, Kuiper Belt, the Heliopause, and the penultimate interstellar precursor mission. For large HPM systems at fixed effective isotropic radiated power, minimum capital cost is achieved when the cost is equally divided between antenna gain and radiated power. This is a driver when considering design of power-beaming systems such as interstellar Beacons, which the Search for Extraterrestrial Intelligence is searching for. Much of the technical means for these applications are already in hand. Microwave and millimeter-wave array antennas are already in use for astronomy; sources at high frequencies are being developed for fusion and the military. Develo- - pment of high-power arrays is needed. A synergistic way to develop a space power-beaming infrastructure is incremental buildup, addressing lower power applications first, and then upgrading.