A central research challenge for the mathematical sciences in the 21st century is the development of principled methodologies for the seamless integration of (often vast) data sets with sophisticated mathematical models. Such data sets are becoming routinely available in almost all areas of engineering, science and technology as well as in commerce and in the social sciences. Furthermore, mathematical models describing phenomena of interest are often built on decades, or even centuries, of human knowledge creation. Ignoring either the data or the models is clearly unwise and so the issue of combining them is of paramount importance. When the underlying mathematical model is a (possibly stochastic) dynamical system, and the data is time-ordered, combining model and data is referred to as data assimilation. Much of the research in this field has been driven by practitioners working in the geophysical sciences. The goal of Stuart's research is to develop systematic theoretical foundations of the subject; these foundations will lead to deeper understanding of the algorithms, improvements in them and in their application to new problem areas beyond the geophysical sciences. Mathematical methodology employed includes high dimensional probability, control theory and dynamical systems.