In the Hydrology Section of the American Geophysical Union, a new Committee on Precipitation was formed in fall 1982 consisting of nine members from the fields of hydrology, atmospheric sciences, statistics, and mathematics. The objective in bringing together these scientists from different disciplines was to collectively address important problems and directions in precipitation research that are of central interest to the long-range development of hydrologic science. It is somewhat trite but true that advances in the stochastic modeling of rainfall require corresponding advances in the understanding of the physical processes which produce precipitation. Consequently, a working dialogue between hydrologists and atmospheric physicists in formulating and addressing research plans seems quite appropriate. In this same spirit, advances in the stochastic modeling of rainfall require advances in mathematical and statistical techniques. Issues pertinent to major unsolved problems and research directions in understanding, modeling, and predicting of precipitation in space and time were extensively discussed among the committee members and are summarized in this article.