During the last decade, distributed ledger solutions such as blockchain have gained significant attention due to their decentralized, immutable, and verifiable features. However, the public availability of data stored on the blockchain and its link to users may raise privacy and security issues. In some cases, addressing these issues requires blockchain data to be secured with mechanisms that allow on-demand (as opposed to full) disclosure. In this paper, we give a comprehensive overview of blockchain privacy and security requirements, and detail how existing mechanisms answer them. We provide a taxonomy of current attacks together with related countermeasures. We present a thorough comparative analysis based on various parameters of state-of the-art privacy and security mechanisms, we provide recommendations to design secure and privacy-aware blockchain, and we suggest guidelines for future research.