© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Blockchain technology has been changing the nature of several businesses, from supply chain management to electronic record management systems and copyright management to healthcare applications. It provides a resilient and secure platform for modifications due to its distributed and shared nature and cryptographic functions. Each new technology, however, comes with its challenges alongside its opportunities. Previously, we performed a systematic literature review (SLR) to explore how blockchain technology potentially benefits health domain applications. The previous SLR included 27 formal literature papers from 2016 to 2020. Noticing that blockchain technology is rapidly growing, we extended the previous SLR with a multivocal literature review (MLR) approach to present the state of the art in this study. We focused on understanding to what degree blockchain could answer the challenges inherited in the health domain and whether blockchain technology may bring new challenges to health applications. The MLR consists of 78 sources of formal literature and 23 sources of gray literature from 2016 to 2021. As a result of this study, we specified 17 health domain challenges that can be categorized into four groups: (i) meeting regulatory requirements and public health surveillance, (ii) ensuring security and privacy, (iii) ensuring interoperability, and (iv) preventing waste of resources. The analysis shows that blockchain makes significant contributions to the solutions of these challenges. However, 10 new pitfalls come with adopting the technology in the health domain: the inability to delete sensitive data once it is added to a chain, limited ability to keep large-scale data in a blockchain, and performance issues. The data we extracted during the MLR is available in a publicly accessible online repository.