As a fundamental method for data mining, data clustering has been widely used in various fields such as computer science, medical science, social science and economics. According to the data distribution of clusters, the data clustering problem can be categorized into linearly separable clustering and nonlinearly separable clustering. Due to the complex manifold of the real-world data, nonlinearly separable clustering is one of the most popular and widely studied clustering problems. In this paper, we will first make a brief survey on the recent research works in nonlinear clustering, from four perspectives, namely, kernel-based clustering, multi-exemplar clustering, graph-based clustering and support vector-based clustering. Then, we will particularly introduce our two research works in nonlinear clustering, namely, position regularized support vector clustering (PSVC) and multi-exemplar affinity propagation (MEAP). We will analyze their merits and limitations and point out the future research directions.