This review covers computer-assisted analysis of images in the field of medical imaging. Recent advances in machine learning, especially with regard to deep learning, are helping to identify, classify, and quantify patterns in medical images. At the core of these advances is the ability to exploit hierarchical feature representations learned solely from data, instead of features designed by hand according to domain-specific knowledge. Deep learning is rapidly becoming the state of the art, leading to enhanced performance in various medical applications. We introduce the fundamentals of deep learning methods and review their successes in image registration, detection of anatomical and cellular structures, tissue segmentation, computer-aided disease diagnosis and prognosis, and so on. We conclude by discussing research issues and suggesting future directions for further improvement.