Recently, there have been increasing calls for healthcare providers to provide controls for patients over their personal health records. Nevertheless, security issues concerning how different healthcare providers exchange healthcare information have caused a flop in the deployment of such systems. The ability to exchange data securely is important so that new borderless integrated healthcare services can be provided to patients. Due to its decentralized nature, blockchain technology is a suitable driver for the much-needed shift towards integrated healthcare, providing new insights and addressing some of the main challenges of many healthcare areas. Blockchain allows healthcare providers to record and manage peer-to-peer transactions through a network without central authority. In this paper, we discuss the concept of blockchain technology and hurdles in their adoption in the healthcare domain. Furthermore, a review is conducted on the latest implementations of blockchain technology in healthcare. Finally, a new case study of a blockchain-based healthcare platform is presented addressing the drawbacks of current designs, followed by recommendations for future blockchain researchers and developers.