The largest tectonic relief breaking the Earth's surface (13 km vertically) is at the subduction margin of the Andes, which generates routinely megathrust earthquakes (Mw > 8.5) and drives the paradigmatic Andean orogen. Here we present key geologic evidence to reassess first-order features of geomorphology and tectonics across the Central Andes, where the orogen includes the Altiplano Plateau and attains its maximum integrated height and width. The Andean subduction margin has a stepped morphology dominated by the low-relief Atacama Bench, which is similar to a giant uplifted terrace, slopes gently over a width of 60-100 km from the Andes to the Pacific, and runs over more than 1000 km of coastal length. We find that the genesis of stepped morphology at the Andean seaboard is due to concomitant development of large west-vergent thrusts parallel to the subduction interface and increasing aridity in the Atacama Desert, which keeps an unprecedented large-scale record of interplaying tectonics and Cenozoic climate change. Incorporating our results with published geological knowledge demonstrates that Andean orogeny is characterized by trench-perpendicular (bivergent) and trench-parallel (bilateral) growth over the past 50 Myr, associated with positive trench velocity toward the continent (trench advance) and subduction of a wide slab under South America. We hypothesize that a global plate tectonic reorganization involving long-lasting viscous mantle flow has probably forced both, Andean orogeny and global climate cooling since 50 Ma. In contrast, two important stepwise pulses of increasing aridity and trench-perpendicular Andean growth appear to be results of changes in erosion rates due to global Late Eocene and Middle Miocene cooling events.