Obtaining depth estimation of a scene from a two-dimensional image is a classic computer vision problem that plays an important role in three-dimensional reconstruction and scene perception. Monocular image depth estimation based on deep learning has been developing rapidly in recent years with new methods being proposed rapidly. This study discusses the application history and research progress in deep learning-based monocular depth estimation and analyzes several representative deep learning algorithms and network architectures in detail for both supervised and unsupervised learning. Finally, the research progress and trend of the deep learning in the monocular depth estimation field are summarized. Existing problems and future research priorities are discussed as well.