Self-Sovereign Identity (SSI), a Blockchain-based technology for digital identity management, is a promising concept for handling health data. It could represent a step forward in empowering users, granting them control over their data. This work conducts a systematic literature review to investigate state-of-the-art measures based on SSI and Blockchain technologies for dealing with electronic health records (EHRs), identifying gaps, and determining the key questions for future research. As a result, this review shows a growing interest in Blockchain methods to handle EHRs, but few works consider using the self-sovereign identity approaches. The results obtained in this work also suggest that: Blockchain technologies provide a viable alternative to deliver EHR solutions such as patient monitoring, healthcare data trading, and prescription control; consolidated Blockchain technologies are the preferred core components of most effective strategies; keeping raw health data off-chain helps to create scalable solutions; health data standards make searching medical records in Blockchain structures feasible; Smart Contracts are essential components of Blockchain-based EHR solutions; the concepts of data ownership and Self-Sovereign Identity have been neither adequately defined nor employed in the health context. CCS Concepts: • Applied computing → Health care information systems; • Security and privacy → Privacy protections; • Computer systems organization → Peer-to-peer architectures; • General and reference → Surveys and overviews.