The spread of health misinformation has the potential to cause serious harm to public health, from leading to vaccine hesitancy to adoption of unproven disease treatments. In addition, it could have other effects on society such as an increase in hate speech towards ethnic groups or medical experts. To counteract the sheer amount of misinformation, there is a need to use automatic detection methods. In this paper we conduct a systematic review of the computer science literature exploring text mining techniques and machine learning methods to detect health misinformation. To organize the reviewed papers, we propose a taxonomy, examine publicly available datasets, and conduct a content-based analysis to investigate analogies and differences among Covid-19 datasets and datasets related to other health domains. Finally, we describe open challenges and conclude with future directions.