Title: Solving and Learning non-Markovian Stochastic Control problems in continuous-time with Neural RDEs. Abstract: We propose a novel framework for solving continuous-time, non-Markovian stochastic control problems with the use of neural rough differential equations (Neural RDEs). By parameterising the control process as the solution of a Neural RDE driven by the state process, we show that the control-state joint dynamics are governed by an uncontrolled RDE with structured vector fields, allowing for efficient trajectories simulation, Monte-Carlo estimation of the value function and backpropagation. To deal with input paths of infinite 1-variation, we refine the existing universal approximation result to a probabilistic density result for Neural RDEs driven by random rough paths. Experiments on various non-Markovian problems indicate how the proposed framework is time-resolution-invariant and capable of learning optimal solutions with higher accuracy than traditional RNN-based approaches. Finally, we discuss possible extensions of this framework to the setting of non-Markovian continuous-time reinforcement learning and provide promising empirical evidence in this direction.