In this talk we discuss Koszul duality from a physics perspective, and emphasize its role in coupling quantum field theories to topological line defects. Using this physical translation of Koszul duality as inspiration, we propose a physical definition of Koszul duality for vertex algebras. The appearances of vertex algebras (physically: holomorphic conformal field theories) in physics are legion; one particularly interesting context in which they appear is (a simplified version of) the three dimensional Anti-de Sitter (AdS)/ two-dimensional conformal field theory (CFT) holographic correspondence. One may be sorely tempted to propose that algebras of operators in AdS and in CFT are Koszul dual to one another in this sense. We will find instead, by studying a popular physical example of AdS(3)/CFT(2), that a deformation of this version of Koszul duality is required to relate the two. (This talk is based on work in collaboration with K. Costello)