Objective To conduct a systematic review of deep learning models for electronic health record (EHR) data, and illustrate various deep learning architectures for analyzing different data sources and their target applications. We also highlight ongoing research and identify open challenges in building deep learning models of EHRs. Design/method We searched PubMed and Google Scholar for papers on deep learning studies using EHR data published between January 1, 2010, and January 31, 2018. We summarize them according to these axes: Types of analytics tasks, types of deep learning model architectures, special challenges arising from health data and tasks and their potential solutions, as well as evaluation strategies. Results We surveyed and analyzed multiple aspects of the 98 articles we found and identified the following analytics tasks: disease detection/classification, sequential prediction of clinical events, concept embedding, data augmentation, and EHR data privacy. We then studied how deep architectures were applied to these tasks. We also discussed some special challenges arising from modeling EHR data and reviewed a few popular approaches. Finally, we summarized how performance evaluations were conducted for each task. Discussion Despite the early success in using deep learning for health analytics applications, there still exist a number of issues to be addressed. We discuss them in detail including data and label availability, the interpretability and transparency of the model, and ease of deployment.