Recent years have seen an explosion in the use of machine learning techniques for studying nonlinear dynamical systems. Here we explore how machine learning can be used to identify and subsequently suppress unknown disturbances to complex systems. We find that unknown disturbances can be accurately detected with reservoir computer architectures even when no knowledge of the underlying dynamics is assumed. All that is required are very mild conditions on the forcing functions used to train the reservoir. Moreover, we also show that this framework can be extended to suppress the disturbances, i.e., controlling the system to recover the undisturbed dynamics. We illustrate our method with the identification of unknown disturbances to an analog electric chaotic circuit as well as numerical simulations of isolated and network-coupled nonlinear systems.