Anosov flows are a class of chaotic dynamical systems that enjoy the remarkable property of being stable under small perturbation. In dimension 3 there is a deep and beautiful connection between the properties of an Anosov flow and the topology of the ambient manifold. For more than twenty years very few examples of Anosov flow were known (geodesic flows and suspension flows). The introduction of surgery techniques allowed us to construct a plethora of new examples with interesting and unexpected properties. Although a connection between Anosov dynamics and contact geometry has been known for decades (by the work of Eliashberg, Mitsumatsu and Thurston), recent work of Hozoori allows us to use powerful tools from the realm of contact structures. In this talk we will use this point of view to address questions in the theory of surgery on Anosov flows.