In 1956, Selberg introduced a zeta function Z(s), a complex function defined in terms of closed geodesics on a negatively curved manifold, by analogy with the Riemann zeta function in number theory. In the case of surfaces with constant negative curvature the Selberg trace formula gives an extension of Z(s) to the entire complex plane. Using a more dynamical approach, and following in the footsteps of Ruelle, Rugh and others, Giulietti, Liverani and I have extended this result to all smooth Anosov flows. In particular, this extends the original result of Selberg to surfaces with variable negative curvature.