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The goals of this review paper on deep learning (DL) in medical imaging and radiation therapy are to (a) summarize what has been achieved to date; (b) identify common and unique challenges, and strategies that researchers have taken to address these challenges; and (c) identify some of the promising avenues for the future both in terms of applications as well as technical innovations. We introduce the general principles of DL and convolutional neural networks, survey five major areas of application of DL in medical imaging and radiation therapy, identify common themes, discuss methods for dataset expansion, and conclude by summarizing lessons learned, remaining challenges, and future directions.