Blockchain can be used to build a peer-to-peer, secure, and smart transaction system. As a horizontal technology that has changed several fields of industry, blockchain has tremendous potential to transform healthcare systems as well. In this article, a systematic review is conducted to critically evaluate 64 articles on blockchain-based healthcare systems, published between 2016 and January 2020 in 21 conferences, 33 journals, and ten online sources. The aim of this article is to answer three main questions. First, what are the applications of blockchain in the healthcare systems, and what are the structures and challenges of applying blockchain to a specific healthcare domain? Second, what are the technical, temporal, and spatial aspects of the currently developed blockchain applications for different healthcare domain? Third, what are the future research directions in designing and implementing blockchain-based healthcare systems? Statistical facts about the technical aspects of these 64 articles show that most of the proposed blockchain-based healthcare systems use private blockchain and Ethereum platforms; furthermore, the majority of the authors are affiliated with research institutions in the USA and China. We also discuss potential future research directions, e.g., integrating the blockchain in artificial intelligence based solutions, cloud-computing-based solutions, and parallel blockchain architecture.