Extending for a length of ~3500 km and reaching elevations of more than 4500 m, the Transantarctic Mountains (TAM) form the main structural and morphological feature of Antarctica that divides the continent into two geological provinces, the stable cratonic block of East Antarctica, and the much younger terrane assemblage of West Antarctica. Already the early Antarctic explorers studied "The Great Antarctic Horst" – as major barrier on their route to the south pole but also for scientific interest. They identified its origin as the largest non-compressional mountain chain on earth but traditional geological methods did not allow to reconstruct the uplift history of the TAM. With the introduction of apatite fission-track analysis a few decades ago, the TAM established as a key area of thermochronological research and the development of tools to convert age and paleo-temperature information into scenarios of exhumation and uplift, and to interpret them in terms of geological processes. Now the published AFT data set of the TAM comprises more that 500 sample ages between ~30 and ~300 Ma and complementary proxy data, collected from up to three km high vertical transects along the whole mountain chain. Thermal history modelling of these age data and proxies in conjunction with the geological record, especially stratigraphic and geomorphological observation, indicates long-term Mesozoic – early Cenozoic heating of the present TAM due to kilometre-scale burial and rapid exhumation and uplift since ~35 Ma. The recognition of the rapid inversion of such an extensive long-lived sedimentary basin is essential for the general understanding of the landscape of Gondwana, the breakup between Antarctica and Australia, and the initiation of the West Antarctic Rift System between West and East Antarctica. Rapid TAM uplift since late Eocene/ early Oligocene times also had primary consequences on floral and faunal radiation, and may have triggered the permanent glaciation of Antarctica, with considerable influence on global long-term climate evolution.