Building extraction from remote sensing (RS) images is a fundamental task for geospatial applications, aiming to obtain morphology, location, and other information about buildings from RS images, which is significant for geographic monitoring and construction of human activity areas. In recent years, deep learning (DL) technology has made remarkable progress and breakthroughs in the field of RS and also become a central and state-of-the-art method for building extraction. This paper provides an overview over the developed DL-based building extraction methods from RS images. Firstly, we describe the DL technologies of this field as well as the loss function over semantic segmentation. Next, a description of important publicly available datasets and evaluation metrics directly related to the problem follows. Then, the main DL methods are reviewed, highlighting contributions and significance in the field. After that, comparative results on several publicly available datasets are given for the described methods, following up with a discussion. Finally, we point out a set of promising future works and draw our conclusions about building extraction based on DL techniques.