Recent advances in deep learning have shown great potential for the automatic generation of medical imaging reports. Deep learning techniques, inspired by image captioning, have made significant progress in the field of diagnostic report generation. This paper provides a comprehensive overview of recent research efforts in deep learning-based medical imaging report generation and proposes future directions in this field. First, we summarize and analyze the data set, architecture, application, and evaluation of deep learning-based medical imaging report generation. Specially, we survey the deep learning architectures used in diagnostic report generation, including hierarchical RNN-based frameworks, attention-based frameworks, and reinforcement learning-based frameworks. In addition, we identify potential challenges and suggest future research directions to support clinical applications and decision-making using medical imaging report generation systems.