We describe a framework to uncover the shape and speed corrections caused by adding noise-terms to PDEs that support travelling wave solutions. We consider both parabolic and dispersive systems, and noise terms that can be Lipschitz or non-Lipschitz. By using perturbative techniques, we avoid the need to use the comparison principle. In some cases, it is no longer sufficient to use the standard linear operators associated to the deterministic travelling waves, which uncovers a surprising connection with singular perturbation theory. Joint work with C. Hamster and R. Westdorp.