The Millimeter Array, being planned by the National Radio Astronomy Observatory (NRAO) in conjunction with the radio astronomy community, will have almost complete coverage of the observable spectrum from 30 to 950 GHz. This paper discusses the choice of frequency bands and describes our present concept of the main receiver components for the MMA, including HFET (heterostructure field-effect transistor) amplifiers for the lower frequencies and sideband separating SIS (superconductor-insulator-superconductor) mixers for higher frequencies. Recent progress on HFET amplifiers has shown them to be competitive with SIS mixers for astronomical applications at frequencies up to approximately 100 GHz. The exact crossover frequency between HFET and SIS receivers in the context of the MMA is not yet determined. HFET receivers for the lower frequencies will be used not only for direct observations, but also for rapid calibration of instrumental and atmospheric phase in 'fast-switching' observing mode. We have already developed cryogenic HFET amplifiers for frequencies up to 110 GHz. Sideband-separating SIS mixers will improve the sensitivity in many spectral line measurements by greatly reducing the effect of atmospheric noise in the image sideband. We have developed an experimental 200 - 300 GHz sideband-separating receiver in which all the RF components -- quadrature hybrid, LO power splitter, LO couplers, and SIS junctions -- are on a single quartz chip. To reduce the effect of sideband noise from the LO source, and also substantially reduce the required LO power, we are developing a balanced SIS mixer, also on a single chip. We plan ultimately to develop a balanced, sideband-separating SIS mixer on a single chip. A first-IF amplifier stage inside the SIS mixer block is expected to eliminate the need for an IF isolator in an SIS receiver, thus permitting a 4 - 12 GHz IF.