As an important boundary-based clustering algorithm, support vector clustering (SVC) can benefit many real applications owing to its capability of handling arbitrary cluster shapes, especially those directly or indirectly related to pattern exploration and description. As the application deepens, the importance of performance (i.e. criterions of accuracy and efficiency) of SVC increases. To identify gaps in the current methods and propose novel research directions for SVC, we present a survey of the literature in this area. Our approach is to classify the most recent advances into either theory or application. For theoretical contributions, advances related to parameter selection and optimization, dual-problem solutions, and cluster labeling are introduced. We also simultaneously summarize the advantages and drawbacks of each study. With respect to applications, we clearly describe eight groups of schemes based on SVC, either as individual or hybrid methods. Finally, we identify the gaps in SVC research and suggest several future research issues and trends.