Passive microwave instruments for remote sensing of the Earth's surface from space can measure many meteorological parameters in the absence of daylight and in the presence of clouds. Because of the large apertures that are required to achieve good spatial resolution (1–5 km) at microwave frequencies, these radiometers should be arrays of small antenna elements that are arranged so that the collecting area of the radiometer is much smaller than that of a conventional, solid scanning antenna with the same spatial resolution. Despite the various methods that might be used for combining the signals from the different array elements and the different ways the elements might be arranged, the sensitivity depends almost exclusively on the collecting area, integration time, RF bandwidth, and the system temperature. Interferometers and phased arrays have limitations on their bandwidths that depend on the size of the array; beam-forming arrays are not so limited. A cross antenna is considered in some detail as an example of a sparse-aperture radiometer. It has 5-km resolution from an 800-km orbit and significantly better sensitivity than the equivalent conically scanning parabolic antenna, while it has only 10% of the collecting area and no moving parts.