This paper presents a new approach to learning for motion planning (MP) where critical regions of an environment are learned from a given set of motion plans and used to improve performance on new environments and problem instances. We introduce a new suite of sampling-based motion planners, Learn and Link. Our planners leverage critical regions to overcome the limitations of uniform sampling, while still maintaining guarantees of correctness inherent to sampling-based algorithms. We also show that convolutional neural networks (CNNs) can be used to identify critical regions for motion planning problems. We evaluate Learn and Link against planners from the Open Motion Planning Library (OMPL) using an extensive suite of experiments on challenging motion planning problems. We show that our approach requires far less planning time than existing sampling-based planners.