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Subcortical structures play a critical role in brain function. However, options for assessing electrophysiological activity in these structures are limited. Electromagnetic fields generated by neuronal activity in subcortical structures can be recorded non-invasively using magnetoencephalography (MEG) and electroencephalography (EEG). However, these subcortical signals are much weaker than those due to cortical activity. In addition, we show here that it is difficult to resolve subcortical sources, because distributed cortical activity can explain the MEG and EEG patterns due to deep sources. We then demonstrate that if the cortical activity can be assumed to be spatially sparse, both cortical and subcortical sources can be resolved with M/EEG. Building on this insight, we develop a novel hierarchical sparse inverse solution for M/EEG. We assess the performance of this algorithm on realistic simulations and auditory evoked response data and show that thalamic and brainstem sources can be correctly estimated in the presence of cortical activity. Our analysis and method suggest new opportunities and offer practical tools for characterizing electrophysiological activity in the subcortical structures of the human brain., Comment: 12 pages with 6 figures