Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) have proved to be extremely valuable tools for the non-invasive study of human brain function. Moreover, due to a notable degree of complementarity between the two modalities, the combination of EEG and fMRI data has been actively sought in the last two decades. Although initially focused on epilepsy, EEG-fMRI applications were rapidly extended to the study of healthy brain function, yielding new insights into its underlying mechanisms and pathways. Nevertheless, EEG and fMRI have markedly different spatial and temporal resolutions, and probe neuronal activity through distinct biophysical processes, many aspects of which are still poorly understood. The remarkable conceptual and methodological challenges associated with EEG-fMRI integration have motivated the development of a wide range of analysis approaches over the years, each relying on more or less restrictive assumptions, and aiming to shed further light on the mechanisms of brain function along with those of the EEG-fMRI coupling itself. Here, we present a review of the most relevant EEG-fMRI integration approaches yet proposed for the study of brain function, supported by a general overview of our current understanding of the biophysical mechanisms coupling the signals obtained from the two modalities.