A Pfaffian variety is a space of anti-symmetric matrices with some fixed upper bound on the rank, and the projective dual of a Pfaffian variety is a another Pfaffian variety. Kuznetsov conjectured that these varieties should have non-commutative resolutions, with the derived categories of projectively-dual pairs satisfying a nice relationship called `homological projective duality’. I will discuss the construction of these NC resolutions (which is due to Spenko and Van den Bergh) and a proof that they do indeed satisfy the duality. Our proof is motivated by a physical duality of non-abelian GLSMs, proposed by Hori. This is joint work with Joergen Rennemo.