In this talk, we show how to reconstruct knot theory in such a way that it is intimately related to quantum physics. In particular, we give a blueprint for creating a quantum system that has the dynamic behavior of a closed knotted piece of rope moving in 3-space. Within this framework, knot invariants become physically measurable quantum observables, knot moves become unitary transformations, with knot dynamics determined by Schroedinger’s equation. The same approach can also be applied to the theory of braids. Possible applications of quantum knots are: (1) The modeling of quantum vortices, and (2) the development of quantum algorithms for topological quantum computing.