Estimating depth from RGB images is a long-standing ill-posed problem, which has been explored for decades by the computer vision, graphics, and machine learning communities. In this article, we provide a comprehensive survey of the recent developments in this field. We will focus on the works which use deep learning techniques to estimate depth from one or multiple images. Deep learning, coupled with the availability of large training datasets, have revolutionized the way the depth reconstruction problem is being approached by the research community. In this article, we survey more than 100 key contributions that appeared in the past five years, summarize the most commonly used pipelines, and discuss their benefits and limitations. In retrospect of what has been achieved so far, we also conjecture what the future may hold for learning-based depth reconstruction research.