The crime prediction model is needed for national security and stability. It is based on police affairs data and temporal-spatial data, predicting cases and events through machine learning. Three aspects are mainly involved in crime prediction: feature selection, prediction method and geographic information visualization. In this paper, the basic ideas of the theory and method of crime predictions are introduced. Besides, based on the generation and evolution of crime, the research results of empirical models and temporal-spatial models are summarized. Then, the strategy of selecting the optimal algorithm is analyzed by different predicted characteristics. Meanwhile, the characteristics of various crime prediction algorithms are compared. In the final part, existing problems and future research directions are analyzed.