Data streams mining, the technology of getting valuable information from continuous data streams is a field that has recently gained increasingly attention all over the world. In the model of data streams, data does not take the form of persistent relations, but rather arrives in a multiple, continuous, rapid and time-varying way. Because of the rapid data arriving speed and huge size of data set in data streams, novel algorithms are devised to resolve these problems. Among these research topics, classifying methods is an important one. In this review paper, the state-of-the-art in this growing vital field is presented, and theses methods are introduced from two directions: stationary distribution data streams and data streams with concept drift. Finally, the challenges and future work in this field are explored.