Earthquake Disaster Assessment (EDA) plays a critical role in earthquake disaster prevention, evacuation, and rescue efforts. Deep learning (DL), which boasts advantages in image processing, signal recognition, and object detection, has facilitated scientific research in EDA. This paper analyses 204 articles through a systematic literature review to investigate the status quo, development, and challenges of DL for EDA. The paper first examines the distribution characteristics and trends of the two categories of EDA assessment objects, including earthquakes and secondary disasters as disaster objects, buildings, infrastructure, and areas as physical objects. Next, this study analyses the application distribution, advantages, and disadvantages of the three types of data (remote sensing data, seismic data, and social media data) mainly involved in these studies. Furthermore, the review identifies the characteristics and application of six commonly used DL models in EDA, including convolutional neural network (CNN), multi-layer perceptron (MLP), recurrent neural network (RNN), generative adversarial network (GAN), transfer learning (TL), and hybrid models. The paper also systematically details the application of DL for EDA at different times (i.e., pre-earthquake stage, during-earthquake stage, post-earthquake stage, and multi-stage). We find that the most extensive research in this field involves using CNNs for image classification to detect and assess building damage resulting from earthquakes. Finally, the paper discusses challenges related to training data and DL models, and identifies opportunities in new data sources, multimodal DL, and new concepts. This review provides valuable references for scholars and practitioners in related fields.