This paper provides analyses of three types of diversity combining systems in practical use. These are: selection diversity, maximal-ratio diversity, and equal-gain diversity systems. Quantitative measures of the relative performance (under realistic conditions) of the three systems are provided. The effects of various departures from ideal conditions, such as non-Rayleigh fading and partially coherent signal or noise voltages, are considered. Some discussion is also included of the relative merits of predetection and postdetection combining and of the problems in determining and using long-term distributions. The principal results are given in graphs and tables, useful in system design. It is seen that the simplest possible combiner, the equal-gain system, will generally yield performance essentially equivalent to the maximum obtainable from any quasi-linear system. The principal application of the results is to diversity communication systems and the discussion is set in that context, but many of the results are also applicable to certain radar and navigation systems.