The objective of streaming data classification is to learn incrementally a decision function that maps input variables to a label variable, from continuously arriving streaming data, so as to accurately classify the test data that may arrive anytime. The online learning paradigm, as an incremental machine learning technology, is an effective tool for classification of streaming data. This paper mainly summarizes, from the perspective of online learning, the recent development of algorithms for streaming data classification. Specifically, the basic framework and the performance evaluation methodology of online learning are first introduced. Then, the latest development of online learning algorithms for general streaming data, for alleviating the "curse of dimensionality" problem in high-dimensional streaming data, and for resolving the "concept drifting" problem in evolving streaming data are reviewed respectively. Finally, future challenges and promising research directions for classification of high-dimensional and evolving streaming data are also discussed.