The optically pumped rubidium maser oscillator is the most recent addition to a growing number of atomic frequency standards. It is the first atomic frequency standard which is small enough and simple enough to be considered as a replacement for crystal oscillators. These factors and the extreme phase stability which results from the maser action make this device unique among all frequency standards. The device generates a microwave output at the ground-state hyperfine frequency of Rb87(6835 Mc/s). The maser consists of a microwave cavity filled with Rb87vapor and nitrogen gas. Oscillation occurs when the vapor is illuminated with filtered rubidium resonance radiation. The power output of the maser is 10-10watts, and higher powers can be expected. In this paper the physical principles and construction of the device are described. The effects of optical pumping, buffer gas, and temperature on the maser are discussed, and experimental results are given. The short-term stability for observation times of about one second is expected to be about one part in 1012. This may be increased by an order of magnitude by increasing the powser output to 10-8watts. The long-term stability is expected to be comparable to that obtained in the passive rubidium standard (about one part in 1011per month). These slow fluctuations arise from pressure shifts, light shifts, cavity pulling, and changes in the chemical composition of the buffer gas. The long-term stability can be improved by using the rubidium maser as the flywheel for an atomic beam frequency standard. Such a combination could be expected to have both long-term and short-term stabilities as great as one part in 1013.