Sebastian Riedel Technische Universität Berlin We present a novel criterion for the existence of Gaussian rough paths in the sense of Friz{Victoir. It is formulated in terms of a covariance measure structure together with a classical condition due to Jain{Monrad. It turns out that this condition is easy to check in many examples which allows for a stochastic calculus for a large class of Gaussian processes, ranging from (bi-)fractional Brownian motion to processes given as random Fourier series. We then discuss two applications. In our rst example we consider the concentration of measure phenomenon on path spaces which can be described using so{called transportation{cost inequalities. We show how rough path theory may be used to establish such inequalities for the law of diusions. Our second example deals with numerics for SDEs driven by Gaussian signals. Namely, we present a multilevel Monte Carlo algorithm which can be applied when calculating the mean of diusion functionals. We show how the multilevel approach helps to reduce the computational complexity considerably compared to a standard Monte Carlo approximation. The rst part of the talk is based on joint work with Peter Friz (TU and WIAS Berlin), Benjamin Gess (Universitat Bielefeld) and Archil Gulisashvili (Ohio University). The last part is joint work with Christian Bayer (WIAS Berlin), Peter Friz (TU and WIAS Berlin) and John Schoenmakers (WIAS Berlin).