Privacy computing technology is a method to protect data privacy, which is characterized by security, efficiency, and sharing, but it inevitably brings the problems of lack of trust in data and lack of incentives for training in the process of data processing, which hinders the wide application of privacy computing. Blockchain technology, as a distributed ledger technology with advantageous features such as decentralization, transparency, and tamper-proof, can help solve the problem of privacy computing limiting the development, while privacy computing can enhance the privacy protection of data on the chain. Therefore, blockchain and privacy computing fusion technology has been widely studied in recent years. Firstly, the basic principles of blockchain and privacy computing were introduced, and then the privacy computing technology was elaborated based on blockchain. In addition, the two directions of blockchain consensus fusion and smart contract fusion based on privacy computing were analyzed in detail. Finally, the possible challenges and key technologies that need to be improved were summarized for the fusion of blockchain and privacy computing.