Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last fifteen years, numerous graph kernels, i.e. kernel functions between graphs, have been proposed to solve the problem of assessing the similarity between graphs, thereby making it possible to perform predictions in both classification and regression settings. This manuscript provides a review of existing graph kernels, their applications, software plus data resources, and an empirical comparison of state-of-the-art graph kernels.