In order to understand how orogens “work,” a quantitative approach demonstrating proof of concept is essential. Our goal is to reconcile the diverse array of tectonic features observed in natural orogens in the context of “working” numerical models that are consistent with both the underlying physics and first-order geological constraints. We present a simple conceptual temperature-magnitude (T-M) framework for orogenesis in terms of the progression from small-cold to large-hot orogens, and we use forward numerical models to test hypotheses corresponding to specific stages along the T-M spectrum. Small-cold orogens are analyzed using crustal-scale singularity (S) point models, in which suborogenic mantle lithosphere is kinematically subducted beneath crust that deforms by critical wedge mechanics. The transition from oceanic subduction to continental collision, and the subsequent evolution of large-hot orogens, has been investigated using both crustal- and upper-mantle–scale models, the latter including dynamic subduction of suborogenic mantle lithosphere. Large-hot orogens with thick crust are characterized by elevated plateaus with a strong superstructure underlain by hot, weak, lower-crustal infrastructure. Beneath plateaus, tectonic processes are dominated by ductile flow of weak crust in response to differential pressure, while plateau flanks form external thrust-sense wedges. We discuss four topical issues in orogenic tectonics, including the response of the suborogenic mantle lithosphere to convergence, the interaction of climate and tectonics, the current debate concerning wedge versus channel-flow models to explain the Himalayan-Tibetan system, and the interpretation of metamorphic architecture in terms of orogenic processes. We conclude that collisional orogenesis is driven largely by subduction and accretion of material at convergent margins, accompanied by shortening, thickening, and heating of deformed crust.