Machine learning and deep learning have provided us with an exploration of a whole new research era. As more data and better computational power become available, they have been implemented in various fields. The demand for artificial intelligence in the field of health informatics is also increasing and we can expect to see the potential benefits of artificial intelligence applications in healthcare. Deep learning can help clinicians diagnose disease, identify cancer sites, identify drug effects for each patient, understand the relationship between genotypes and phenotypes, explore new phenotypes, and predict infectious disease outbreaks with high accuracy. In contrast to traditional models, its approach does not require domain-specific data pre-process, and it is expected that it will ultimately change human life a lot in the future. Despite its notable advantages, there are some challenges on data (high dimensionality, heterogeneity, time dependency, sparsity, irregularity, lack of label) and model (reliability, interpretability, feasibility, security, scalability) for practical use. This article presents a comprehensive review of research applying deep learning in health informatics with a focus on the last five years in the fields of medical imaging, electronic health records, genomics, sensing, and online communication health, as well as challenges and promising directions for future research. We highlight ongoing popular approaches' research and identify several challenges in building deep learning models.