With its central position between the Tibetan Plateau and the Tian Shan Range, the Tarim Basin is a key element of the Cenozoic Asian orogenic system. However, a comprehensive regional study, and more particularly the quantification of shortening through this basin and its margins, are still needed to understand its role in the Cenozoic deformation of Asia. From a compilation of previous works, together with an extensive dataset of satellite, field, seismic and well data, we provide a tectonic map of the Cenozoic structures and four balanced geological transects of the Tarim Basin and its surrounding ranges. Based on this map and these cross-sections, we characterize the Cenozoic deformation of the original Proterozoic Tarim block. From structural restorations and crustal budgets, we also quantify the compressive component of this deformation. Most of the Cenozoic compressive deformation (from ~94% to 100%) is concentrated in the ranges along the block margins. To the west, up to 78 ± 23 km and 54 +24/-18 km of crustal shortening are accommodated across the compressive Western Kunlun and Southwestern Tian Shan ranges, while to the east, up to 38.6 ± 18 km and 15 +20/-15 km are accommodated across the transpressive Altyn Tagh and Southeastern Tian Shan ranges. A non-negligible amount of compressive deformation (up to ~6%) is also accommodated within the Tarim Basin by large basement-cored uplifts with a vergence synthetic to the deformation of the Tibetan Plateau edge. To the west, the Bachu uplift absorbs ~5 km of the total crustal shortening of the Western Kunlun thrust system, while to the south, the Tanan uplift accumulates ~0.6 km of the Altyn Tagh strike-slip system. Structural inheritance has a major influence on the Cenozoic deformation since ~33.3% to 100% of the total shortening is accommodated by reactivated basement structures inherited from the Protero-Paleozoic history of the Tarim block. Finally, we argue that the basement-cored uplifts in the centre of the basin imply a deformation transfer from the Tibetan Plateau to the Tian Shan, above a deep crustal decollement decoupling the deforming crust from an underlying rigid mantle.