In natural environments, visual and auditory stimulation elicit responses across a large set of brain regions in a fraction of a second, yielding representations of the multimodal scene and its properties. The rapid and complex neural dynamics underlying visual and auditory information processing pose major challenges to human cognitive neuroscience. Brain signals measured non-invasively are inherently noisy, the format of neural representations is unknown, and transformations between representations are complex and often nonlinear. Further, no single non-invasive brain measurement technique provides a spatio-temporally integrated view. In this opinion piece, we argue that progress can be made by a concerted effort based on three pillars of recent methodological development: (i) sensitive analysis techniques such as decoding and cross-classification, (ii) complex computational modelling using models such as deep neural networks, and (iii) integration across imaging methods (magnetoencephalography/electroencephalography, functional magnetic resonance imaging) and models, e.g. using representational similarity analysis. We showcase two recent efforts that have been undertaken in this spirit and provide novel results about visual and auditory scene analysis. Finally, we discuss the limits of this perspective and sketch a concrete roadmap for future research.