We aim at providing a comprehensive introduction to Support Vector Machines and their applications in computational finance. Based on the advances of the statistical learning theory, one of the first SVM algorithms was proposed in mid 1990s. Since then, they have drawn a lot of research interests both in theoretical and application domains and have became the state-of-the-art techniques in solving classification and regression problems. The reason for the success is not only because of their sound theoretical foundation but also their good generalization performance in many real applications. In this chapter, we address the theoretical, algorithmic and computational issues and try our best to make the article selfcontained. Moreover, in the end of this chapter, a case study on default prediction is also presented. We discuss the issues when SVM algorithms are applied to bankruptcy prognosis such as how to deal with the unbalanced dataset, how to tune the parameters to have a better performance and how to deal with large scale dataset.