The southernmost Andes form an orocline, between the Patagonian cordillera, trending N–S, and the Fueguian cordilleras, trending E–W. On the foreland side is the Magellan Basin. The area has a history of Paleozoic compression, Triassic to Early Cretaceous rifting and Late Cretaceous to Quaternary compression, in response to changing plate tectonics. Major structures of Late Cretaceous and Cenozoic age vary along the strike. In the Patagonian cordillera and foothills, folds and thrusts trend NNW, slightly oblique to the orogen, whereas strike–slip faults are parallel to the orogen and right-lateral. In the Fueguian cordilleras and foothills, folds and thrusts trend ESE, slightly oblique to the orogen, whereas strike–slip faults are parallel to the orogen and left-lateral. In the axial zone of the Magellan Basin, folds and thrusts are parallel to the orogen and rifts are sub-perpendicular to it. To a first approximation, the pattern of structures has mirror symmetry about the axis of the Magellan Basin. In detail, however, wrenching appears to be more prevalent in the Fueguian cordillera and foothills, than it is in the Patagonian cordillera and foothills. Minor faults of Cenozoic age are common in the foothills. From a kinematic analysis of fault–slip data: (1) shortening and stretching directions are mostly sub-horizontal; (2) shortening directions vary in trend, from ENE in the Patagonian foothills, to NE in the Fueguian foothills; and (3) stretching directions are sub-parallel to traces of major thrusts. In the Fueguian cordillera and foothills, strike–slip faulting is prevalent; in the Patagonian foothills, crustal thickening is prevalent over strike–slip faulting. The kinematics reflect a combination of thrusting and wrenching and they are consistent with the major structures. To investigate the origin of the Cenozoic structures, we used analogue models on a fully lithospheric scale, where an oceanic plate subducted beneath a continental corner. The corner was an area of transition, from frontal subduction, to transcurrent motion. The boundary conditions may not have been fully realistic, but the experiments did account for the major elements of the structural pattern in southernmost South America, including rifts that are perpendicular to the orogen and counterclockwise block rotations.