Blockchain has been widely deployed in various sectors, such as finance, education, and public services. Since blockchain runs as an immutable distributed ledger, it has decentralized mechanisms with persistency, anonymity, and auditability, where transactions are jointly performed through cryptocurrency-based consensus algorithms by worldwide distributed nodes. There have been many survey papers reviewing the blockchain technologies from different perspectives, e.g., digital currencies, consensus algorithms, and smart contracts. However, none of them have focused on the blockchain data management systems. To fill in this gap, we have conducted a comprehensive survey on the data management systems, based on three typical types of blockchain, i.e., standard blockchain, hybrid blockchain, and DAG (Directed Acyclic Graph)-based blockchain. We categorize their data management mechanisms into three layers: blockchain architecture, blockchain data structure, and blockchain storage engine, where block architecture indicates how to record transactions on a distributed ledger, blockchain data structure refers to the internal structure of each block, and blockchain storage engine specifies the storage form of data on the blockchain system. For each layer, the works advancing the state-of-the-art are discussed together with technical challenges. Furthermore, we lay out the future research directions for the blockchain data management systems.