Data assimilation—the set of techniques whereby information from observing systems and models is combined optimally—is rapidly becoming prominent for study of the Earth system, especially for climate predictions. This chapter presents the broad principles of data assimilation, details the main approaches (Bayesian methods, Optimal Interpolation, 3Dand 4D-variational methods, and Kalman filter), and then outlines some practical applications of the exploitation of geophysical data by data assimilation in oceanography and atmospheric sciences.