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Soil structure pertains to the spatial arrangement of voids and solid constituents, their aggregation, and mechanical state. As a fragile product of soil biological activity that includes invisible ingredients (mechanical and ecological states), soil structure is difficult to define rigorously, and measurements of relevant metrics often rely on core samples or on episodic point measurements. The presence of soil structure has not yet been explicitly incorporated in climate and Earth systems models, partially due to incomplete methodological means to characterize it at relevant scales and to parameterize it in spatially extensive models. We seek to review the potential of harnessing geophysical methods to fill the scale gap in characterization of soil structure directly (via impact of soil pores, transport, and mechanical properties on geophysical signals) or indirectly by measurement of surrogate variables (wetness and rates of drainage). We review basic aspects of soil structure and challenges of characterization across spatial and temporal scales and how geophysical methods could be used for the task. 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