We present both a scientific overview and conceptual positions concerning the challenges and assets of electrophysiological measurements in the search for the nature and functions of the human connectome. We discuss how the field has been inspired by findings and approaches from functional magnetic resonance imaging (fMRI) and informed by a small number of significant multimodal empirical studies, which show that the canonical networks that are commonplace in fMRI are in fact rooted in electrophysiological processes. This review is also an opportunity to produce a brief, up-to-date critical survey of current data modalities and signal processing methods available for deriving both static and dynamic connectomes using electrophysiological data. We review hurdles that challenge the significance and impact of current electrophysiology connectome research. We then encourage the field to take a leap of faith and embrace the wealth of electrophysiological signals, despite their apparent, disconcerting complexity. Our position is that electrophysiology connectomics is poised to inform testable mechanistic models of information integration in hierarchical brain networks, constructed from observable oscillatory and aperiodic signal components and their polyrhythmic interactions.

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