Anthropogenic atmospheric aerosols (suspended particulate matter) can modify the radiative balance (and climate) of the Earth by altering the properties and global distribution of clouds. Current climate models however cannot adequately account for many important aspects of these aerosol-cloud interactions, ultimately leading to a large uncertainty in the estimation of the magnitude of the effect of aerosols on climate. This thesis focuses on the development of physically-based descriptions of aerosol-cloud processes in climate models that help to address some of such predictive uncertainty. It includes the formulation of a new analytical parameterization for the formation of ice clouds, and the inclusion of the effects of mixing and kinetic limitations in existing liquid cloud parameterizations. The parameterizations are analytical solutions to the cloud ice and water particle nucleation problem, developed within a framework that considers the mass and energy balances associated with the freezing and droplet activation of aerosol particles. The new frameworks explicitly account for the impact of cloud formation dynamics, the aerosol size and composition, and the dominant freezing mechanism (homogeneous vs. heterogeneous) on the ice crystal and droplet concentration and size distribution. Application of the new parameterizations is demonstrated in the NASA Global Modeling Initiative atmospheric and chemical and transport model to study the effect of aerosol emissions on the global distribution of ice crystal concentration, and, the effect of entrainment during cloud droplet activation on the global cloud radiative properties. The ice cloud formation framework is also used within a parcel ensemble model to understand the microphysical structure of cirrus clouds at very low temperature. The frameworks developed in this work provide an efficient, yet rigorous, representation of cloud formation processes from precursor aerosol. They are suitable for the study of the effect of anthropogenic aerosol emissions on cloud formation, and can contribute to the improvement of the predictive ability of atmospheric models and to the understanding of the impact of human activities on climate.