In this technically advanced era, we are surrounded by smartphones, computers, and cameras, which help us to store visual information in 2D image planes. However, such images lack 3D spatial information about the scene, which is very useful for scientists, surveyors, engineers, and even robots. To tackle such problems, depth maps are generated for respective image planes. Depth maps or depth images are single image metric which carries the information in three-dimensional axes, i.e., xyz coordinates, where z is the object's distance from camera axes. For many applications, including augmented reality, object tracking, segmentation, scene reconstruction, distance measurement, autonomous navigation, and autonomous driving, depth estimation is a fundamental task. Much of the work has been done to calculate depth maps. We reviewed the status of depth map estimation using different techniques from several papers, study areas, and models applied over the last 20 years. We surveyed different depth-mapping techniques based on traditional ways and newly developed deep-learning methods. The primary purpose of this study is to present a detailed review of the state-of-the-art traditional depth mapping techniques and recent deep learning methodologies. This study encompasses the critical points of each method from different perspectives, like datasets, procedures performed, types of algorithms, loss functions, and well-known evaluation metrics. Similarly, this paper also discusses the subdomains in each method, like supervised, unsupervised, and semi-supervised methods. We also elaborate on the challenges of different methods. At the conclusion of this study, we discussed new ideas for future research and studies in depth map research.