In this article, we review recent uses of convolutional neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object classification and segmentation tasks. Motivated by these successes, researchers have begun to apply CNNs to the resolution of inverse problems such as denoising, deconvolution, superresolution, and medical image reconstruction, and they have started to report improvements over state-of-the-art methods, including sparsity-based techniques such as compressed sensing. Here, we review the recent experimental work in these areas, with a focus on the critical design decisions: From where do the training data come? What is the architecture of the CNN? How is the learning problem formulated and solved? We also mention a few key theoretical papers that offer perspectives on why CNNs are appropriate for inverse problems, and we point to some next steps in the field.