Astronomical studies of celestial sources at low radio frequencies (0.3 to 30 MHz) lag far behind the investigations of celestial sources at high radio frequencies. In a companion paper [Basart et al., this issue] we discussed the need for low-frequency investigations, and in this paper we discuss the telescopes required to make the observations. Radio telescopes for use in the low-frequency range can be built principally from “off-the-shelf” components. For relatively little cost for a space mission, great strides can be made in deploying arrays of antennas and receivers in space that would produce data contributing significantly to our understanding of galaxies and galactic nebulae. In this paper we discuss an evolutionary sequence of telescopes, antenna systems, receivers, and (u, v) plane coverage. The telescopes are space-based because of the disruptive aspects of the Earth's ionosphere on low-frequency celestial signals traveling to the Earth's surface. Orbiting antennas consisting of array elements deposited on a Kevlar balloon have strong advantages of nearly identical multiple beams over 4π steradians and few mechanical aspects in deployment and operation. The relatively narrow beam width of these antennas can significantly help reduce the “confusion” problem. The evolutionary sequence of telescopes starts with an Earth-orbiting spectrometer to measure the low-frequency radio environment in space, proceeds to a two-element interferometer, then to an orbiting array, and ends with a telescope on the lunar farside. The sequence is in the order of increasing capability which is also the order of increasing complexity and cost. All the missions can be accomplished with current technology.