Kernel-based learning methods are primarily used with real-valued data. Yet many domains are made up of structured objects such as strings, trees or graphs. This work focuses on the design of kernels capable of coping with structured objects. It briefly introduces kernel-based learning methods and kernel theory, and goes on to study the basic mechanisms for kernel combination and the family of convolution kernels, which is meant as the main building block for a theory of kernels on structured domains. Additionally, some practical design strategies are identified through applications of the theory. Finally, some proposals are outlined aimed at future research.