Classification of images acquired by airborne and satellite sensors is a very challenging problem. These remotely sensed images usually acquire information from the scene at different wavelengths or spectral channels. The main problems involved are related to the high dimensionality of the data to be classified and the very few existing labeled samples, the diverse noise sources involved in the acquisition process, the intrinsic nonlinearity and non‐Gaussianity of the data distribution in feature spaces, and the high computational cost involved to process big data cubes in near real time. The framework of statistical learning in general, and of kernel methods in particular, has gained popularity in the last decade. New methods have been presented to address all these problem specificities. We will review the main existing algorithmic proposals to cope with the spatial homogeneity of images, to take advantage of the manifold structure with semisupervised learning, to encode invariances, and to deal with one‐class and multitemporal problems. The design of a suitable regularized functional has led to the successful solution of many remote sensing image classification problems. This article reviews the main advances for remote sensing image supervised classification with kernels through illustrative examples.