Abstract: Sleep stage classification based on physiological signals is essential for monitoring sleep and diagnosing sleep disorders. Artificial sleep stage classification method is time-consuming, inefficient, and subjective. In recent years, automatic sleep stage classification method has attracted more attention due to its efficiency and accuracy. Therefore, the automatic sleep stage classification algorithms are reviewed from the past six years based on the perspective of algorithm. The literature is classified as traditional machine learning and deep learning, and each category is further summarized based on single- and multi-channel physiological signal inputs, illustrating algorithms, signal types, and sleep staging performance. Comparison across the methods indicates that the single-channel input reduces the cost of signal acquisition, making it more suitable for home sleep monitoring. The multi-channel input is closer with sleep staging guidelines, which is more appropriate for clinical analysis. Compared with traditional machine learning methods, deep learning methods offer more promising researching prospects, because they utilize deep neural networks to automatically learn representation, which efficiently handle large-scale dataset and provide better sleep staging performance. Existing works demonstrate that the future sleep staging research of deep learning should focus more on improving model interpretability and generalization instead of model design, to promote the application of deep neural networks in sleep medicine field.