Recent years have witnessed the unprecedented progress of deep learning applications in digital holography (DH). Nevertheless, there remain huge potentials in how deep learning can further improve performance and enable new functionalities for DH. Here, we survey recent developments in various DH applications powered by deep learning algorithms. This article starts with a brief introduction to digital holographic imaging, then summarizes the most relevant deep learning techniques for DH, with discussions on their benefits and challenges. We then present case studies covering a wide range of problems and applications in order to highlight research achievements to date. We provide an outlook of several promising directions to widen the use of deep learning in various DH applications.