Support Vector Machine (SVM) is one of the best techniques to classify the data into multiple classes. In the recent years, support vector machine has been used extensively for classification problems. The main advantage of using support vector machines is its better generalization ability while using higher dimension of data. This paper gives a review on the formulation of some important variants of SVM i.e. hard margin SVM, soft margin SVM, Least Squares Support Vector Machine (LSSVM), Twin Support Vector Machine (TWSVM) and Least Squares Support Vector Machine (LS-TWSVM). To check the effectiveness of these methods, numerical experiments are performed on artificial and real world datasets.