Support vector machines and kernel methods belong to the same class of machine learning algorithms that has recently become prominent in both computational biology and chemistry, although both fields have largely ignored each other. These methods are based on a sound mathematical and computationally efficient framework that implicitly embeds the data of interest, respectively proteins and small molecules, in high-dimensional feature spaces where various classification or regression tasks can be performed with linear algorithms. In this review, we present the main ideas underlying these approaches, survey how both the "biological" and the "chemical" spaces have been separately constructed using the same mathematical framework and tricks, and suggest different avenues to unify both spaces for the purpose of in silico chemogenomics.