An overview of Kernel Methods, which are crucial tools for solving non-linear machine learning problems, is given in this presentation. We will quickly introduce the necessary Functional Analysis theory and immediately apply these concepts to classical algorithms like regression and Principal Component Analysis. Kernel Analog Forecasting (KAF) will be the main application covered, showing how it can be used to model dynamical systems, especially in climate science. The practical limitations of kernel methods will be critically assessed at the end of the talk.