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Twin support vector machine (TWSVM) has gained increasing interest from various research fields recently. In this paper, we aim to report the current state of the theoretical research and practical advances on TWSVM. We first give the basic thought and theory of TWSVM, including the theory of proximal support vector machine, generalized eigenvalue proximal support vector machine, and TWSVM. Then, we focus on the various improvements made to TWSVM, mainly including least squares twin support vector machine, smooth twin support vector machine, regularized twin support vector machine, projection twin support vector machine, and modified TWSVM on the model selection problem. These newly emerging algorithms greatly expand the applications of TWSVM. In recent years, there is a lot of research on application of TWSVM. Next, we list some research on application of TWSVM in detail. Finally, we try to provide a comprehensive view of these advances in TWSVM and discuss the direction of future research. [ABSTRACT FROM AUTHOR]