Clouds govern the balances of radiation and energy in the atmosphere. Cloud microphysical processes determine transformation of cloud particles and precipitation formation, and are accompanied by phase transitions and latent heat release determining dynamics of clouds and large-scale processes. A major method of investigating clouds and cloud-related phenomena is numerical modeling that implies solving coupled dynamic and microphysical equations for different processes occurring in clouds. The book presents a systematic analysis of modern theories of major microphysical processes in warm, mixed-phase and ice clouds, with the focus on representation of these process in state-of-the-art numerical cloud models and cloud resolving models, as well as on the perspectives of further development and applications of these models. We also analyze numerical approaches to solving microphysical and dynamic equations in spectral bin microphysics schemes and bulk parameterization schemes. The book is intended as a comprehensive reference for students, researchers and numerical model designers in the fields of Cloud Physics, Atmospheric Science, Environmental Sciences, and Meteorology.