Inverse modeling has many applications in oceanography and meteorology. Charts or “analyses” of temperature, pressure, currents, winds and the like are needed for operations and research. The analyses should be based on all our knowledge of the ocean or atmosphere, including both timely observations and the general principles of geophysical fluid dynamics. Analyses may be needed for flow fields that have not been observed, but which are dynamically coupled to observed fields. The data must therefore contribute not only to the analyses of observed fields, but also to the inference of corrections to the dynamical inhomogeneities which determine the coupled fields. These inhomogeneities or inputs are: the forcing, initial values and boundary values, all of which are themselves the products of imperfect interpolations. In addition to input errors, the dynamics will inevitably contain errors owing to misrepresentations of phenomena that cannot be resolved computationally; the data are therefore also required to improve the dynamics by adjusting the empirical coefficients in the parameterizations of the unresolved phenomena. Conversely, the model dynamics must have some credibility, and should be allowed to influence assessments of the effectiveness of observing systems. Finally, and perhaps most compelling of all, geophysical fluid dynamical models need to be formulated and tested as formal scientific hypotheses, so that the development of increasingly realistic models may proceed in an orderly and objective fashion. All of these needs can be met by inverse modeling.