In recent years, with the popularity of cloud services, increasingly more enterprises and individuals have stored their data in cloud databases. However, enjoying the convenience of cloud services also brings about data security issues. One of the crucial problems is data confidentiality protection, which is to safeguard the sensitive data of users from being spied on or leaked. Fully encrypted databases have emerged to face this challenge. Compared with traditional databases, fully encrypted databases can encrypt data in the entire lifecycle of data transmission, storage, and computation, thereby ensuring data confidentiality. Currently, there are still many challenges in encrypting data while supporting all SQL functionalities and maintaining high performance. This study comprehensively investigates the key techniques of encrypted computing in fully encrypted databases, summarizes the techniques according to the types, and compares and sums up them based on functionality, security, and performance. Firstly, it introduces the architecture of fully encrypted databases, including crypto-based architecture, trusted execution environment (TEE)-based architecture, and hybrid architecture. Then, the key techniques of each architecture are summarized. Finally, the challenges and opportunities of current research are discussed, with some open problems provided for future research.