Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2. Alternatively, one can proceed by flow decomposition and this approach also works in a number of non-linear situations. Secondly, now motivated by some semi-linear SPDEs of Burgers’ type with infinite-dimension noise, we study the stochastic heat equation (in space dimension 1) as evolution in Gaussian rough path space relative to the spatial variable, in the sense of Chap. 10.