The Arabia-Eurasia collision deforms an area of ~3,000,000 km2 of continental crust, making it one of the largest regions of convergent deformation on Earth. There are now estimates for the active slip rates, total convergence and timing of collision-related deformation of regions from western Turkey to eastern Iran. This paper shows that extrapolating the present day slip rates of many active fault systems for ~3--7 million years accounts for their total displacement. This result means that the present kinematics of the Arabia-Eurasia collision are unlikely be the same as at its start, which was probably in the early Miocene (16--23 Ma) or earlier. In some, but not all, active fault systems, short-term (~10 year) and long-term (~5 million year) average deformation rates are consistent. There is little active thickening across the Turkish-Iranian plateau and, possibly, the interior of the Greater Caucasus. These are two areas where present shortening rates would need more than 7 million years to account for the total crustal thickening, and where there are structural and/or stratigraphic data for pre-late Miocene deformation. We suggest that once thick crust (up to 60 km) built up in the Turkish-Iranian plateau and the Greater Caucasus, convergence took place more easily by crustal shortening in less elevated regions, such as the Zagros Simple Folded Zone, the South Caspian region and foothills of the Greater Caucasus, or in other ways, such as westward transport of Turkey between the North and East Anatolian faults. The time and duration of this changeover are not known for certain and are likely be diachronous, although deformation started or intensified in many of the currently active fault systems at ~5 ¿ 2 Ma.