This talk is divided into two parts: In the first part, I will review the impact that kernel methods have had in remote sensing image and data processing during the last decade, while the second part foresees the future developments grounded on deep learning machines. Part 1: Kernel methods constitute a simple way of translating linear algorithms into nonlinear ones. I will review the main aspects of kernel methods and their advantages for RS data processing, and will pay attention to our recent kernel developments for: 1) classification and change detection problems that consider the class-specific features; 2) noise-resistant nonlinear feature extraction methods; 3) regression and dependence estimation in Bayesian nonparametrics; and 4) multidimensional image quality assessment with kernels. The introduced methods extend previous standard algorithms to deal with non-stationary environments and structured domains, and assumptions about the noise nature. Examples in image processing will guide this overview. Part 2: Deep learning is a new field of machine learning that alleviates many problems of kernel machines, and has provided outstanding results in pattern recognition, speech recognition, bioinformatics and natural language processing. I will review their main features and introduce some recent developments in my group to perform 1) multidimensional image density estimation, saliency, multi-information estimation and anomaly detection via data multi-layered Gaussianization, and 2) multi- and hyperspectral image classification with semisupervised large scale neural networks.