We have studied the Cenozoic and active tectonics of the north-eastern rim of Tibet west of the Yellow River (Gansu, China) where the western Haiyuan Fault enters the eastern Qilian Shan, a high mountainous region, which was the site of the 1927 May 23, M = 8-8.3, Gulang earthquake. Fieldwork, combined with analysis of aerial photographs and satellite images, reveals consistent cumulative left-lateral offsets of postglacial geomorphic features along the fault, but no recent rupture. West of the Tianzhu pull-apart basin, the levelling of offset-terrace risers implies Holocene horizontal and vertical slip rates on the steeply south-dipping, N110E-striking fault of 11 +/- 4 and 1.3 +/- 0.3 mm yr(-1), respectively. The presence of subordinate, mostly normal, throws due to local changes in fault strike, and kinematic compatibility at the SW corner of the Tianzhu basin, constrains the azimuth of the fault-slip vector to be N110-115E. On the less prominent, N85-100E-striking Gulang Fault, which splays eastwards from the Haiyuan Fault near 102.2 degrees E, less detailed observations suggest that the average Holocene left-slip rate is 4.3 +/- 2.1 mm yr(-1) with a minor component of approximate to N-directed thrusting, with no recent seismic break either. East of approximate to 103 degrees E, coeval slip on both faults thus appears to account for as much as 15 +/- 6 mm yr(-1) of left-lateral movement between NE Tibet and the southern edge of the Ala Shan Platform, in a N105 +/- 6E direction. West of approximate to 103 degrees E, structural and geomorphic evidence implies that approximate to NNE-directed shortening of that edge across the rising, north-eastern Qilian mountain ranges occurs at a rate of 4 +/- 2 mm yr(-1), by movement on right-stepping thrusts that root on a 10-20 degrees S-dipping decollement that probably branches off the Haiyuan Fault at a depth of approximate to 25 km. The existence of fresh surface breaks with metre-high free faces on a N-dipping, hanging-wall normal fault south of the easternmost, Dongqingding thrust segment, and of half-metre-high pressure ridges on that segment, indicates that the 1927 Gulang earthquake ruptured that complex thrust system. The approximate to 4 mm yr(-1) shortening rate is consistent with the inference that the thrusts formed and move as a result of orthogonal slip partitioning in a large restraining bend of the Haiyuan Fault. Based on a retrodeformable structural section, we estimate the cumulative shortening on the Qilian Shan thrusts, north of the Haiyuan Fault, to be at least 25 km. The finite displacements and current slip rates on either the thrusts or the left-lateral faults imply that Cenozoic deformation started in the Late Miocene, with slip partitioning during much of the Plio-Quaternary. Assuming coeval slip at the present rates on the Haiyuan and Gulang Faults in the last 8 Ma would bring the cumulative left-lateral displacement between NE Tibet and the Ala Shan Platform to about 120 km, consistent with the 95 +/- 15 km offset of the Yellow River across the Haiyuan Fault, but many times the offset (approximate to 16 km) inferred on one recent strand of that fault east of the river. Relative to the SE Gobi Desert, NE Tibet thus appears to have moved by a fair amount in the Late Cenozoic and is still moving fast. While some of this motion probably contributes to displace (towards the ESE) and rotate (CCW) the south-west edge of the Ordos block, much of it appears to be transmitted to the South China block, which leads, with the additional contribution of other large left-slip faults to the south and despite thrusting in the Lungmen Shan, to the extrusion (towards the ESE-SE) of that block relative to the Gobi, hence to north-eastern Asia. The approximate to 260 km long western Haiyuan Fault links two faults that ruptured about 70 years ago during two great earthquakes only seven years apart. Despite spectacular evidence of Holocene movement, it bears no trace of a large earthquake in the past eight centuries, either in the field or in the historical record. Given its relatively high slip rate, it should therefore be singled out as one of the most critical sites for impending great earthquakes (at least M greater than or equal to 7.5, probably M greater than or equal to 8) in the region. That such a seismic gap, called here the 'Tianzhu gap', lies only approximate to 100 km north of Lanzhou and Xining, largest population centres of west-central China, makes instrumental monitoring of that fault particularly urgent. That the M approximate to 8, Gulang earthquake ruptured a complex thrust surface under high mountains in a restraining bend of the Haiyuan strike-slip fault suggests that the occurrence of comparable earthquakes in other areas with similar fault geometry, such as south of the big bend of the San Andreas Fault in California, should not be ruled out.