We review the growing use of machine learning in electron microscopy (EM) driven in part by the availability of fast detectors operating at kiloHertz frame rates leading to large data sets that cannot be processed using manually implemented algorithms. We summarize the various network architectures and error metrics that have been applied to a range of EM-related problems including denoising and inpainting. We then provide a review of the application of these in both physical and life sciences, highlighting how conventional networks and training data have been specifically modified for EM.