Support vector machine (SVM) has been successfully applied in classification and regression problems. But it is very sensitive to the selection of parameters. The fundamental principles of SVM are analyzed firstly. The main optimization methods and achievements for SVM parameters are introduced. And the popular fitness functions used for the parameter optimization of SVM are described. The objective of this paper is to provide readers a brief overview of the recent advances for parameter optimization of SVM and enable them to develop and implement new optimization strategies for SVM-related research at their disposal.