Multimodal data are ubiquitous in engineering, communications, robotics, computer vision, or more generally speaking in industry and the sciences. All disciplines have developed their respective sets of analytic tools to fuse the information that is available in all measured modalities. In this paper, we provide a review of classical as well as recent machine learning methods (specifically factor models) for fusing information from functional neuroimaging techniques such as: LFP, EEG, MEG, fNIRS, and fMRI. Early and late fusion scenarios are distinguished, and appropriate factor models for the respective scenarios are presented along with example applications from selected multimodal neuroimaging studies. Further emphasis is given to the interpretability of the resulting model parameters, in particular by highlighting how factor models relate to physical models needed for source localization. The methods we discuss allow for the extraction of information from neural data, which ultimately contributes to 1) better neuroscientific understanding; 2) enhance diagnostic performance; and 3) discover neural signals of interest that correlate maximally with a given cognitive paradigm. While we clearly study the multimodal functional neuroimaging challenge, the discussed machine learning techniques have a wide applicability, i.e., in general data fusion, and may thus be informative to the general interested reader.