We present a coherent treatment, based on linear kinetic theory, of stochastic radiative transfer in an atmosphere containing clouds. A brief summary of statistical cloud radiation models is included. We explore the sensitivities inherent in the stochastic approach by using a well-known plane-parallel model developed by Fouquart and Bonnel together with our own stochastic model which generalizes earlier work of F. Malvagi, R. N. Byrne, G. C. Pomraning, and R. C. J. Somerville. In overcast conditions, in comparison to the plane parallel model, the stochastic model underestimates transmittance at small optical depths (<7) and overestimates transmittance at large optical depths. The stochastic model is strongly sensitive to cloud optical properties, including cloud water content and cloud droplet effective radius. The extension of the stochastic approach to an atmospheric general circulation model parameterization appears to be most appropriate for cloud fraction ranging from 25 to 70%. We conclude that stochastic theory holds substantial promise as a modeling approach for calculating shortwave radiative transfer through partially cloudy fields. Unlike cloud-resolving models and Monte Carlo cloud models, stochastic cloud models do not depend on specific realizations of the cloud field. Instead, they calculate the transfer of radiation through a cloudy atmosphere whose properties are known statistically in the form of probability density functions characterizing cloud geometry and cloud optical properties. The advantage of the stochastic approach is its theoretical generality and its potential for representing a complex cloud field realistically at modest computational cost.