Model Theory and Complex Geometry

Model theory is a branch of mathematical logic whose techniques have proven to be useful in several disciplines, including algebra, algebraic geometry and number theory. The last fifteen years have also seen the application of model theory to bimeromorphic geometry, which is the study of compact complex manifolds up to bimeromorphic equivalence. In this article I will try to explain why logic should have anything to say about compact complex manifolds. My primary focus will be on the results in bimeromorphic geometry obtained by model-theoretic methods and the questions about compact complex manifolds that model theory poses.