Depth estimation is a classic task in computer vision, which is of great significance for many applications such as augmented reality, target tracking and autonomous driving. Traditional monocular depth estimation methods are based on depth cues for depth prediction with strict requirements, e.g. shape-from-focus/ defocus methods require low depth of field on the scenes and images. Recently, a large body of deep learning methods have been proposed and has shown great promise in handling the traditional ill-posed problem. This paper aims to review the state-of-the-art development in deep learning-based monocular depth estimation. We give an overview of published papers between 2014 and 2020 in terms of training manners and task types. We firstly summarize the deep learning models for monocular depth estimation. Secondly, we categorize various deep learning-based methods in monocular depth estimation. Thirdly, we introduce the publicly available dataset and the evaluation metrics. And we also analysis the properties of these methods and compare their performance. Finally, we highlight the challenges in order to inform the future research directions.