  Knot contact homology studies symplectic and contact geometric properties of
conormals of knots in 3-manifolds using holomorphic curve techniques. It has
connections to both mathematical and physical theories. On the mathematical
side, we review the theory, show that it gives a complete knot invariant, and
discuss its connections to Fukaya categories, string topology, and micro-local
sheaves. On the physical side, we describe the connection between the
augmentation variety of knot contact homology and Gromov-Witten disk
potentials, and discuss the corresponding higher genus relation that quantizes
the augmentation variety.
