The study of high energy density plasmas (for example those produced with high powered laser systems) is important for our understanding of astrophysics, nuclear fusion and fundamental physics — however, the nonlinearities and strong couplings present in these extreme physical systems makes them very difficult to understand theoretically or to optimize experimentally. In this talk I will discuss how machine learning models and data-driven methods are in the process of reshaping our exploration of these extreme systems. From a fundamental perspective, our understanding can be improved by the way in which machine learning models can rapidly discover complex interactions in large datasets. From a practical point of view, the newest generation of extreme physics facilities can perform experiments multiple times a second (as opposed to approximately daily), thus moving away from human-based control towards automatic control based on real-time interpretation of diagnostic data and updates of the physics model. To make the most of these emerging opportunities, we suggest proposals for the community. This talk summarises Hatfield et al., (2021) https://www.nature.com/articles/s41586-021-03382-w, the findings of a Lorentz Centre meeting in January 2020.