Computer systems at the security and management level play a role in the era called Digital health. Thus, security processes in the medical field benefit health service providers, their administrators, and registered patients with an electronic medical record (EHR) since the information belongs to them. Smart contracts, in conjunction with blockchain technology, are a way to work and improve these security components associated with EHR. This manuscript describes different proposals presented by researchers where smart contracts are used for authentication and entry into a system, as well as a brief comparison between the proposed algorithms, their performance in terms of time and concurrency, and the security tests carried out to confirm system security. This paper also verifies the open issues and proposed future works described by the different authors.