Several novel and robust learning algorithms, with the aim to overcome the drawbacks of traditional clustering algorithms, are developed for data clustering and its applications. The effectiveness and superiority of the proposed methods are supported by experimental results. 1) Te proposed RDA exhibits several robust clustering characteristics: robust to the initialization, robust to cluster volumes, and robust to noise and outliers.2) The proposed IFCSS algorithm achieves two robust clustering characteristics: the robustness against noisy points is obtained by the maximization of mutual information, and the optimal cluster number is auto-determined by the VC-bound induced cluster validity.3) The KDA is developed to discover some complicated (e.g., linearly nonseparable) data structures which can not be revealed by traditional clustering methods in the standard Euclidean space.4) Finally, robust clustering methods have been developed for image segmentation and pattern classification. The proposed ASDA can perform unsupervised clustering for robust image segmentation. The KPCM is developed to generate weights used for SVM training.