This chapter focuses on assimilation of observations from satellites, which is a dominant source of observation information in weather and climate. This includes satellite radiances, both clear sky and all-sky. The most important challenges of all-sky radiances come from their connection to cloud microphysics, which potentially implies nonlinear, non-Gaussian, and nondifferentiable processes that are difficult for data assimilation. The complexity of error covariance with microphysical variables is illustrated in a few real-world examples. An additional difficulty with assimilating all-sky radiances comes from correlated observation errors that require special attention in data assimilation. Practical ways to deal with correlated observation errors are described. Nonlinearity and nondifferentiability of observation operators for all-sky radiances is also briefly explained. Since satellite radiance observations and observation operators generally contain bias, a common formulation of radiance bias correction methods is also presented. The observations from satellites also include radio occultation and lightning observations, as well as satellite products.