Face forgery technology has made considerable progress in recent years, and has several challenges in terms of maintaining social stability and protecting individual rights. Nowadays, an ordinary person can easily generate lifelike fake images and videos, including fake news related to public figures, without any professional knowledge. To eliminate the social security risks caused by fake face images and videos, face forgery detection has become an emerging field that has attracted considerable attention. This survey provides a detailed overview of face forgery and face forgery detection methods. Based on the ratio of manipulations to the original image,this paper first introduces four types of face forgery methods: i) identity swap, ii) expression swap, iii) attribute manipulation, iv) entire face synthesis, and corresponding face forgery detection datasets. We then introduce image- and video-level face forgery detection methods. To improve the manipulation detection results, most face forgery detection methods exploit prior knowledge, such as biological and frequency information, based on deep learning. Subsequently, this paper analyzes the effects of these manipulation detection methods. Finally, we discuss the shortcomings of the current methods in terms of practical applications and discuss the future development trend of face forgery detection.