With the rapid growth of textual content on the Internet, efficient large-scale semantic text retrieval has garnered increasing attention from both academia and industry. Text hashing, which projects original texts into compact binary hash codes, is a crucial method for this task. By using binary codes, the semantic similarity computation for text pairs is significantly accelerated via fast Hamming distance calculations, and storage costs are greatly reduced. With the advancement of deep learning, deep text hashing has demonstrated significant advantages over traditional, data-independent hashing techniques. By leveraging deep neural networks, these methods can learn compact and semantically rich binary representations directly from data, overcoming the performance limitations of earlier approaches. This survey investigates current deep text hashing methods by categorizing them based on their core components: semantic extraction, hash code quality preservation, and other key technologies. We then present a detailed evaluation schema with results on several popular datasets, followed by a discussion of practical applications and open-source tools for implementation. Finally, we conclude by discussing key challenges and future research directions, including the integration of deep text hashing with large language models to further advance the field. The project for this survey can be accessed at https://github.com/hly1998/DeepTextHashing.