Guided depth map super-resolution (GDSR), which aims to reconstruct a high-resolution (HR) depth map from a low-resolution (LR) observation with the help of a paired HR color image, is a longstanding and fundamental problem, it has attracted considerable attention from computer vision and image processing communities. A myriad of novel and effective approaches have been proposed recently, especially with powerful deep learning techniques. This survey is an effort to present a comprehensive survey of recent progress in GDSR. We start by summarizing the problem of GDSR and explaining why it is challenging. Next, we introduce some commonly used datasets and image quality assessment methods. In addition, we roughly classify existing GDSR methods into three categories, i.e., filtering-based methods, prior-based methods, and learning-based methods. In each category, we introduce the general description of the published algorithms and design principles, summarize the representative methods, and discuss their highlights and limitations. Moreover, the depth related applications are introduced. Furthermore, we conduct experiments to evaluate the performance of some representative methods based on unified experimental configurations, so as to offer a systematic and fair performance evaluation to readers. Finally, we conclude this survey with possible directions and open problems for further research. All the related materials can be found at https://github.com/zhwzhong/Guided-Depth-Map-Super-resolution-A-Survey.CCS Concepts: • General and reference → Surveys and overviews.