As critical Internet infrastructure, DNS brings many privacy and security risks due to its plaintext transmission. Many encryption technologies for DNS channel transmission, such as DoH, DoT, and DoQ, are committed to preventing DNS data from leaking or tampering and ensuring the reliability of DNS message sources. Firstly, this study analyzes the privacy and security problems of plaintext DNS from six aspects, including the DNS message format, data storage and management, and system architecture and deployment, and then summarizes the existing related technologies and protocols. Secondly, the implementation principles and the application statuses of the encryption protocols for DNS channel transmission are analyzed, and the performance of each encryption protocol under different network conditions is discussed with multi-angle evaluation indicators. Meanwhile, it discusses the privacy protection effects of the encryption technologies for DNS channel transmission through the limitations of the padding mechanism, the encrypted traffic identification, and the fingerprint-based encryption activity analysis. In addition, the problems and challenges faced by encryption technologies for DNS channel transmission are summarized from the aspects of the deployment specifications, the illegal use of encryption technologies by malicious traffic and its attack on them, the contradiction between privacy and network security management, and other factors affecting privacy and security after encryption. Relevant solutions are also presented. Finally, it summarizes the highlights of future research, such as the discovery of the encrypted DNS service, server-side privacy protection, the encryption between recursive resolvers and authoritative servers, and DNS over HTTP/3.