This paper is a critical survey of the measurement of rainfall by remote sensors. It is shown that single-parameter radar rainfall measurements are limited because both reflectivity and rain rate are dependent on at least two parameters of the drop size distribution, viz., representative raindrop size and number concentration. Simulations are presented which use experimental raindrop size spectra and show the improvement in accuracy attainable through the use of combinations of two and three remote measurables. The spectrum of remote measurables is then reviewed. These include path integrated techniques of radiometry and of microwave and optical attenuation. A carefully designed short-path microwave attenuation experiment which employs these techniques is sufficiently persuasive to show that the disappointing results achieved in many others was due largely to a combination of rain sampling problems and vertical air motions between the path and the gages. Other experiments reviewed show that when paths are colinear, attenuation deduced from radar and radiometry is in good agreement with that measured directly. Several dual-wavelength radar methods are described which were aimed at improved measurements in small range increments but have produced generally disappointing results. However, when the total path attenuation estimated in this way, or by radiometry, is used as a constraint on the retrieval of rain profiles from the radar, the results are more promising. Selected experiments involving combinations of two or more of the three measurables, radar reflectivity Z, attenuation, and/or radiometry, show considerable promise when adequate account is taken of the sampling and air motion problems. The best results in gate-by-gate measurements have been achieved with dual polarization or differential reflectivity (ZDR). However, even these are subject to potentially large errors when the rainfall does not behave according to a priori assumptions embodied in the technique. An accompanying paper in this issue shows that the use of a third remote parameter in addition to Z and ZDR offers great promise. With a growing appreciation of the needs and the capabilities of the various techniques, the future of highly improved remote rainfall measurements seems bright.