Increasing volumes of digital data, combined with advances in visualization, allow for a new three‐dimensional (3D) conceptualization of modern subduction systems. Here we present 16 visual exploration sessions with the ShowEarthModel program that interrogate modern slab morphologies on Earth. These virtual voyages through the Earth's interior provide a snapshot into the four‐dimensional evolution of plate tectonics, captured by the modern state of slab structure. Examining the modern subduction system in an interactive 3‐D framework provides an improved conceptualization of the morphology of slabs. The movies demonstrate that unlike the modern mid‐ocean ridge system, modern subduction systems are laterally discontinuous features, making lateral slab edges prevalent. The 3‐D visualizations elucidate the manner in which slabs intersect and overlap, processes that occur in at least six of the Earth's major subduction zones. The observed variability within a given subduction zone as well as the physical presence of intersecting slabs suggests that slab gaps and slab windows are common. The 3‐D rendering shows relative differences in the radius of curvature for arcuate slabs, as well as the variability in dip within a given subduction zone. Addressing the complex geometries of subducted lithosphere in this way can place constraints on outstanding questions of subduction dynamics including slab strength, mantle rheology, mantle flow circulation, and plate‐asthenosphere coupling. By conceptualizing the modern subduction system on Earth in 3‐D space, this paper contributes to the paradigm shift from a two‐dimensional (2‐D) to 3‐D framework for interpreting the subduction process.