I review how two dimensional dilaton gravities arise in various
contexts, e.g. from dimensional reduction in general relativity and as low
energy effective action in type 0A string theory. All these models are
classically integrable. Semi-classically the Hawking effect arises from
the conformal anomaly. Non-perturbative path integration over geometry and
dilaton is possible and leads to non-local, non-polynomial effective
matter actions. Results for the lowest order S-matrix for s-wave
gravitational scattering are presented.
