The crustal structure of the Eastern Alps and adjacent tectonic units investigated in this work sheds new light on the relationship of surface geology to geodynamic processes operating at depth. Of particular interest are the nature of a previously proposed Moho gap south and east of the Tauern Window, the plate tectonic affinity of the steeply dipping Eastern Alpine slab, and the relationship of the Alps to the Neogene sedimentary basins and the Bohemian Massif. To address these questions, we use various seismological approaches based on converted waves from the temporary passive experiment EASI (Eastern Alpine Seismic Investigation), a complementary experiment of the AlpArray project. The EASI is a densely spaced, 540 km long seismic network along 13.3°E we operated for more than a year. The uppermost-crustal structures in and near the Alps exhibit dipping layers and/or tilted anisotropy that correlate well with surface geology observations. The Moho, despite its variable appearance, is clearly identified along most of the swath. The Variscan lithospheric blocks beneath the Bohemian Massif are imaged with sub-vertical boundaries. Beneath the Eastern Alps, the shape of the Moho is consistent with bi-vergent orogenic thickening, with a steeper and deeper-reaching Adriatic plate plunging northwards beneath the European plate in the north. At the junction of these plates at depth, around the previously proposed Moho gap, the root of the Eastern Alps is a broad trough characterized by a zone of low velocity-gradient that is up to 20 km thick, transitioning between crust and mantle. Our receiver-function results corroborate earlier lithosphere-upper mantle seismic tomography images, and highlight the Adriatic affinity of the Eastern Alpine slab. The zigzag deployment pattern of stations in the EASI experiment also allows distinction of short-wavelength variations perpendicular to the profile, both within the shallow and the deep crust. This underlines the importance of applying 3D imaging in complex geodynamic systems.