Deep learning has enabled the development of fast surrogate models for complex geophysical systems and, through their adjoints, made it possible to perform variational data assimilation with them. I will illustrate these advances using both deterministic and stochastic surrogates trained on a state-of-the-art physical sea-ice model. These surrogates are stable, accurate, and physically consistent, and can be integrated into an operational sea-ice data assimilation and forecasting system. In a second example, I will show that sequential data assimilation itself can be learned, leading to methods that are significantly more efficient and robust than current state-of-the-art approaches. This, in turn, opens new algorithmic directions for the theory of data assimilation.