In the study of space-time rainfall it is particularly important to establish characteristic properties to guide both theoretical and modeling research efforts. In the present paper, new observational analyses on the scaling properties of time-evolving cumulated rainfall fields are presented, and a theoretical framework for their interpretation is introduced. It is found that the time evolution of the spatial organization of a cumulated rainfall field produces scaling relationships of spatial Variance versus time and characteristic values for the scaling exponent. The reproduction of these Values constitutes a basic requirement for spatial-temporal field generators in order to model important properties of real rainfall fields. It is then shown, on theoretical grounds, what properties the instantaneous rainfall intensity fields must obey in order to reproduce the experimental observations and how the size of the observation domain affects the scaling relationships. Some current stochastic models of space-time precipitation are finally discussed and analyzed in the light of the tools introduced, to show under what circumstances the models considered give acceptable results. Furthermore, it is shown that the assumption of an exponential time correlation function, used in many current rainfall models, is not compatible with observations.