Food safety is an important public health issue, and deep learning (DL) algorithms can provide powerful tools and methods for food safety and authenticity detection. Compared with chemometric algorithms and traditional machine learning algorithms, the performances of DL algorithms are improved in many aspects. By learning and analyzing a large amount of data, DL models can improve the efficiency and accuracy of food safety and authenticity detection, helping to ensure the public health and safety. This paper reviews some commonly used chemometric algorithms, traditional machine learning algorithms, and popular DL algorithms. Among them, special attentions are paid to convolutional neural network (CNN), fully convolutional network (FCN) and generative adversarial network (GAN). Moreover, the auxiliary effect of GAN on CNN is highlighted. Finally, this paper revisits recent applications of DL algorithms in the field of food safety and authenticity detection, and prospects the challenges and future directions of DL algorithms in this field. Although DL has made many achievements in the field of food safety and authenticity detection, there is still a great potential for development. For example, the data augmentation function of GAN can assist CNN to obtain more training samples, thus improving the recognition rate. In addition, multimodal neural network (MNN) or multimodal attention network (MAN) can be also used to achieve the fusion of data from different modalities to further improve the robustness and accuracy of DL algorithms. Display omitted •Some popular DL algorithms in food safety and authenticity detection are introduced.•The improvements of DL algorithms to chemometric and ML algorithms are summarized.•Recent applications of DL algorithms in food safety and authenticity detection are reviewed.•Future prospects of DL algorithms in food safety and authenticity detection are discussed.