Model theory is a branch of mathematical logic that uses tools from logic in order to explore mathematical structures (models). When those structures are of geometric nature, we tend to call this study "tame geometry". We will give a broad introduction to tame geometry, and survey some topics at the nexus of model theory and: (a) Diophantine geometry, focusing on recovering algebraic curves from "definable" sets with many rational points, (b) group theory, on a definable version of Hilbert's 5th problem, and (c) extremal combinatorics, around the Vapnik-Chervonenkis theory and its links to statistical learning (time permitting).