Abstract. Deep learning-based depth estimation has become an important topic in recent years, not only in the field of computer vision. Also in the context of remote sensing, scientists started a few years ago to adapt or develop suitable approaches to realize a reconstruction of the Earth’s surface without requiring several images. There are many reasons for this: First, of course, the aspect of general economization, since especially high-resolution satellite images are often accompanied by high data acquisition costs. In addition, there is also the desire to be able to acquire high-quality geoinformation as quickly as possible in time-critical cases – for example, the provision of up-to-date maps for emergency forces in disaster scenarios. Finally, a reconstruction of topography based only on single images can also provide important approximate values for the classic multi-image methods. For example, various processing steps in a classical InSAR process chain require a rough knowledge of the Earth’s surface in order to achieve the most accurate and reliable results. In this paper, we review the developments documented in the remote sensing literature so far. Using an established neural network architecture, we produce example results for both very-high-resolution SAR and optical imagery. The comparison shows that SAR-based single-image-height reconstruction seems to bear an even greater potential than single-image height reconstruction from optical data.