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