Machine learning and pattern recognition techniques are being increasingly employed in functional magnetic resonance imaging (fMRI) data analysis. By taking into account the full spatial pattern of brain activity measured simultaneously at many locations, these methods allow detecting subtle, non-strictly localized effects that may remain invisible to the conventional analysis with univariate statistical methods. In typical fMRI applications, pattern recognition algorithms "learn" a functional relationship between brain response patterns and a perceptual, cognitive or behavioral state of a subject expressed in terms of a label, which may assume discrete (classification) or continuous (regression) values. This learned functional relationship is then used to predict the unseen labels from a new data set ("brain reading"). In this article, we describe the mathematical foundations of machine learning applications in fMRI. We focus on two methods, support vector machines and relevance vector machines, which are respectively suited for the classification and regression of fMRI patterns. Furthermore, by means of several examples and applications, we illustrate and discuss the methodological challenges of using machine learning algorithms in the context of fMRI data analysis.