Kernel methods are the third generation techniques for pattern analysis tasks such as pattern classification, regression and clustering. Kernel based learning methods enable analysis of nonlinear patterns with the efficiency as that of linear methods. The key aspects of kernel methods are as follows [1]: Data items on which pattern analysis is to be carried out are embedded into a vector space called the kernel feature space. Then optimal linear relations are sought among the images of the data items in the feature space. Pattern analysis techniques are implemented in such a way that the coordinates of the embedded points are not needed, and only their pair-wise inner products are needed. The pair-wise inner products can be computed efficiently directly from the original data items using a Mercer kernel function. Another important aspect of kernel methods is that they can also be applied on non-vectorial types of data such as graphs, sets, texts, strings, graphs and trees. Performance of kernel methods is dependent on the choice of the kernel. Design of a suitable Mercer kernel for the data on which the pattern analysis task is to be carried out is an important issue in kernel methods. Support vector machine is a kernel based method for 2-class pattern classification that involves construction of maximal margin hyperplane in the kernel feature space. Multi-class pattern classification is realized using the one-against-the-rest approach or the one-against-one approach. Support vector regression is a kernel based method for nonlinear regression that uses an e-insensitive loss function as the cost function to be minimized. Kernel based clustering [2] involves minimization of the trace of the scatter matrix of the embedded data items in the kernel feature space for separation of nonlinearly separable clusters in the data space. We present the applications of support vector machines, support vector regression and kernel based clustering for speech and image processing tasks. We demonstrate the effectiveness of kernel methods for tasks such as recognition of subword units of speech [3], speaker change detection and online handwritten character recognition for Indian language scripts.