Blockchains provide a decentralized, permanent, and verifiable ledger that can record transactions having digital properties, leading to a fundamental shift in various revolutionary scenarios, such as smart cities, eHealth, or eGovernment. Blockchain has a wide variety of applications in healthcare that can enhance mobile health applications, tracking devices, exchanging, and storing electronic medical records, clinical trial data, and insurance information storage. The survey covers privacy strategies in public and unauthorized blockchains, e.g., Bitcoin and Ethereum, and privacy-preserving research ideas and solutions in both public and private blockchains. We also take into account various blockchain scenarios such as privacy-preserving identity management systems and platforms. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.