Portions of seismic lines and a structure-contour map illustrate the patterns and shapes of salt diapirs and related structures in the Campos and Santos areas, off the Atlantic coast of Brazil. We interpret the structures both kinematically and mechanically, drawing on our experience with similar salt structures worldwide, with the results of recent physical modelling and with geometric restorations in section and in plan. Salt diapirs and related structures have a variety of structural styles, distributed in domains and provinces. Near the coast, there is an upper domain, 100–200 km wide, with a suite of structures that we attribute to horizontal downdip extension: these are salt rollers, in the footwalls of listric normal growth faults; salt walls of triangular cross section, beneath intersecting conjugate normal faults; turtle anticlines; and salt welds. Downslope extension started in the Albian and has continued to the present day. In the Campos area, from simple line balancing, the accumulated downslope displacement is about 100 km. Seawards of this, there is a lower domain, 100–400 km wide, with a different suite of structures, that we attribute to downdip contraction: these are growth folds of various wavelengths, in sedimentary sequences of various thicknesses; asymmetric salt walls, emplaced above reverse faults; deep basins, wedged down between conjugate reverse faults; and salt tongues above thrusts. For Campos, we estimate the total downslope contraction, accumulated since the Albian, to be about 100 km. From the balance between extension and contraction, we infer that the thin-skinned salt tectonics are gravitationally driven and independent of any basement tectonics. The structure-contour map on the top of the salt shows that structural style is variable also along strike. Seismic sections along regional contours indicate differing amounts of strain. On this basis, we distinguish five provinces, separated by NW-SE-trending lines. For the Northern Campos province, we infer radially convergent gliding; for the Campos or Cabo Frio provinces, radially divergent gliding; and for Northern Santos, divergent gliding at a large scale. The pattern in Southern Santos is complicated by right-lateral wrenching against the southern edge of the salt.