Inferences about brain function, using functional neuroimaging data, require models of how the data were derived. A variety of models are used in practice that range from conceptual models of functional anatomy to nonlinear mathematical models of hemodynamic responses (e.g. as measured by functional magnetic resonance imaging, fMRI) and neuronal responses. In this review, we discuss the most important models used to analyse functional imaging data and demonstrate how they are interrelated. Initially, we briefly review the anatomical foundations of current theories of brain function on which all mathematical models rest. We then introduce some basic statistical models (e.g. the general linear model) used for making classical (i.e. frequentist) and Bayesian inferences about where neuronal responses are expressed. The more challenging question, how these responses are caused, is addressed by models that incorporate biophysical constraints (e.g. forward models from the neural to the hemodynamic level) and/or consider causal interactions between several regions, i.e. models of effective connectivity. Some of the most refined models to date are neuronal mass models of electroencephalographic (EEG) responses. These models enable mechanistic inferences about how evoked responses are caused, at the level of neuronal subpopulations and the coupling among them.