Model theory is going through something of a golden age right now, with striking applications in different areas of mathematics, including combinatorics, non-archimedean geometry, transcendence theory, and arithmetic dynamics. Much of these applications have motivated further developments in pure model theory, and vice versa. The goal of this thematic programme is to push forward the spectacular applications of model theory of the past decade while at the same time nurturing the internal developments in the subject upon which these applications depend. We aim to bring together the inward-looking and outward-looking practitioners of the discipline.