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The Support Vector Machine has gained significant popularity over recent years as a kernel-based supervised learning technique. However, choosing the appropriate kernel function and its associated parameters is not a trivial task. The kernel is often chosen from several widely-used and general-purpose functions, and the parameters are then empirically tuned for the best results on a specific data set. This paper explores the use of Particle Swarm Optimization and Genetic Programming as evolutionary approaches to evolve effective kernel functions for a given dataset. Rather than using expert knowledge, we evolve kernel functions without human-guided knowledge or intuition. Our results show consistently better SVM performance with evolved kernels over a variety of traditional kernels on several datasets.