Remote Health Monitoring (RHM) is going to reinvent the future healthcare industry and bring about abundant value to hospitals, doctors, and patients by overcoming the many challenges currently being faced in monitoring patient's well-being, promoting preventive care, and managing the quality of drugs and equipment. Despite the many benefits of RHM, it is yet to be widely deployed due to the healthcare data security and privacy challenges. Healthcare data are highly sensitive and require fail-safe measures against unauthorized data access, leakages, and manipulations, and as such, there are stringent regulations governing how healthcare data can be secured, communicated, and stored, such as General Data Protection Regulation (GDPR) and the Health Insurance Portability and Accountability Act (HIPAA). The challenges and regulatory demands in RHM applications can be addressed using blockchain technology due to its distinguishing features of decentralization, immutability, and transparency to address the challenges of data security and privacy. This article will provide a systematic review on the use of blockchain in RHM, focusing primarily on data security and privacy.