Abstract: In nature, the deep forest (DF) algorithm opened the deep learning model of non-neural network structure firstly. Due to the characteristics of non-differential form-based learners and without requiring a large amount of training data, DF has become an important direction in the industry and academic domain. Thus, the existing DF algorithm was generalized and summarized, in which its main structure and characteristics were reviewed. First, the structure and properties of DF were introduced. Further, the current research was classed into five research directions, i.e., introducing feature engineering, improving representation learning, modifying base learner, modifying the hierarchical structure, and introducing weight configuration, which were analyzed and summarized, respectively. Then, the state of the art application status of DF algorithms in different fields was introduced and the challenges and future research direction of the DF algorithm were proposed. Finally, the work of this paper was summarized.