I'll describe a new link between supersymmetric gauge theories, with gauge group G, and the Yangian for the Lie algebra of G. The main result is that a certain twisted, deformed N=1 supersymmetric gauge theory, with gauge group G, is "controlled" by the Yangian built from G, in the same way that Chern-Simons theory is controlled by the quantum group. This statement holds to all orders in perturbation theory, and there is a similar result for pure N=2 and N=4 gauge theories. This result has many concrete corollaries: as an example, I will explain how to calculate certain vacuum expectation values of Wilson operators using the representation theory of the Yangian.