Koszul duality in quantum field theory

In this article, we introduce basic aspects of the algebraic notion Koszul duality for a physics audience. We then review its appearance in physical problem coupling QFTs to topological line defects, and illustrate concept with some examples drawn from twists various simple supersymmetric theories. Though much content article is well-known experts, presentation have not, our knowledge, appeared literature before. Our aim provide an elementary introduction those interested gauge theories defects and, ultimately, generalizations higher-dimensional twisted holography.