Deep learning provides exciting solutions in many fields, such as image analysis, natural language processing, and expert system, and is seen as a key method for various future applications. On account of its non-invasive and good soft tissue contrast, in recent years, Magnetic Resonance Imaging (MRI) has been attracting increasing attention. With the development of deep learning, many innovative deep learning methods have been proposed to improve MRI image processing and analysis performance. The purpose of this article is to provide a comprehensive overview of deep learning-based MRI image processing and analysis. First, a brief introduction of deep learning and imaging modalities of MRI images is given. Then, common deep learning architectures are introduced. Next, deep learning applications of MRI images, such as image detection, image registration, image segmentation, and image classification are discussed. Subsequently, the advantages and weaknesses of several common tools are discussed, and several deep learning tools in the applications of MRI images are presented. Finally, an objective assessment of deep learning in MRI applications is presented, and future developments and trends with regard to deep learning for MRI images are addressed.