Abstract: Statistical learning theory is the statistical theory of smallsample, and it focuses on the statistical law and the nature of learning of small samples. Support vector machine is a new machine learning method based on statistical learning theory, and it has become the research field of machine learning because of its excellent performance. This paper describes the theoretical basis of support vector machines (SVM) systematically, sums up the mainstream machine training algorithms of traditional SVM and some new learning models and algorithms detailedly, and finally points out the research and development prospects of support vector machine.