The development of electronic health records (EHR) systems has enabled the collection of a vast amount of digitized patient data. However, utilizing EHR data for predictive modeling presents several challenges due to its unique characteristics. With the advancements in machine learning techniques, deep learning has demonstrated its superiority in various applications, including healthcare. This survey systematically reviews recent advances in deep learning-based predictive models using EHR data. Specifically, we introduce the background of EHR data and provide a mathematical definition of the predictive modeling task. We then categorize and summarize predictive deep models from multiple perspectives. Furthermore, we present benchmarks and toolkits relevant to predictive modeling in healthcare. Finally, we conclude this survey by discussing open challenges and suggesting promising directions for future research.