Face recognition is one of the important applications of computer vision, which plays an important role in production and life. The first half of this article explains the traditional face recognition algorithms, focusing on the PCA and LDA algorithms based on dimensionality reduction and the hand-designed LBP operator and HOG features. The basic principles are briefly outlined and their advantages and disadvantages are explained. Convolutional neural networks are widely used in face recognition. The second half is mainly based on deep learning algorithms. Several types of classic face recognition algorithms are summarized. For the first time, the DeepID algorithm using convolutional neural networks is proposed and used for the first time. The FaceNet algorithm with the concept of triples, the well-known residual network reduces network parameters. These algorithms have improved the accuracy of face recognition to varying degrees.