The inherent asymmetry of extension by detachment leads to contrasting and conjugate classes of passive margins. Upper‐plate margins comprise crust above a deeper detachment. Lower‐plate margins comprise the footwall of the detachment, overlain by faulted upper plate remnants. Such margins have distinctive architectures, structural styles, uplift‐subsidence paths and thermal histories. The wide range in structural styles on passive margins is predicted by five models which incorporate detachment faults linked to flat ductile shear zones, and ductile stretching of the thermal lithosphere below the shear zones. These models provide explanations for enigmatic structural and morphological features of passive margins such as marginal plateaux, outer highs, unstructured synrift sag basins, and perched rift basins. Numerical modelling of isostatic uplift‐subsidence histories shows that different patterns of uplift‐subsidence behaviour can be explained by variations in detachment geometry and change in the amount of lithospheric stretching. Voluminous igneous underplating is predicted if anomalously hot asthenosphere is uplifted. The arrival of such mantle derived melts may cause significant additional uplift. Upper‐plate margins undergo thermally induced uplift, with permanent uplift due to igneous underplating. This uplift may be the origin of passive margin mountains in the adjacent hinterlands. Marginal plateaux are emergent or very shallowly submerged throughout the extension history, with postrift subsidence to intermediate water depths. The lithosphere is extended below a midcrustal detachment, but with little extension of the upper‐plate. The pattern of subsidence on an Atlantic margin requires an extended upper plate superimposed on progressively more stretched subdetachment lithosphere. Conjugate margins are described from the Tasman Sea, the Atlantic Ocean and the Great Southern Ocean, illustrating both the principle of complementary asymmetry and the different patterns of uplift or subsidence on opposing passive margins.