Functional magnetic resonance imaging (fMRI) is used to investigate where the neural implementation of specific cognitive processes occurs. The standard approach uses linear convolution models that relate experimentally designed inputs, through a haemodynamic response function, to observed blood oxygen level dependent (BOLD) signals. Such models are, however, blind to the causal mechanisms that underlie observed BOLD responses. Recent developments have focused on how BOLD responses are generated and include biophysical input-state-output models with neural and haemodynamic state equations and models of functional integration that explain local dynamics through interactions with remote areas. Forward models with parameters at the neural level, such as dynamic causal modelling, combine both approaches, modelling the whole causal chain from external stimuli, via induced neural dynamics, to observed BOLD responses.