Deep reinforcement learning (DRL) augments the reinforcement learning framework, which learns a sequence of actions that maximizes the expected reward, with the representative power of deep neural networks. Recent works have demonstrated the great potential of DRL in medicine and healthcare. This paper presents a literature review of DRL in medical imaging. We start with a comprehensive tutorial of DRL, including the latest model-free and model-based algorithms. We then cover existing DRL applications for medical imaging, which are roughly divided into three main categories: (i) parametric medical image analysis tasks including landmark detection, object/lesion detection, registration, and view plane localization; (ii) solving optimization tasks including hyperparameter tuning, selecting augmentation strategies, and neural architecture search; and (iii) miscellaneous applications including surgical gesture segmentation, personalized mobile health intervention, and computational model personalization. The paper concludes with discussions of future perspectives.