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The aim of this review paper is to describe the impact of so-called border traps (BTs) in high- k gate oxides on the operation and reliability of high-mobility channel transistors. First, a brief summary of the physics of BTs will be given, describing the charge trapping and release in terms of the elastic tunneling model. It will be also pointed out how information on the BT properties can be extracted from popular measurement techniques such as low-frequency (1/f) noise and variable-frequency charge pumping. In the next two parts, the impact of BTs on metal-oxide-semiconductor structures fabricated on Ge or III-V channel materials is outlined, with particular emphasis on the development of novel or adapted measurement techniques such as AC transconductance dispersion or trap spectroscopy by charge injection and sensing. Finally, the effect of BTs on the operation and reliability of high-mobility channel MOSFETs is discussed. It is also shown that the density of BTs is closely linked to the quality or defectivity of the high- k gate stack, indicating room for improvement by optimization of processing or by implementation of a suitable bulk-oxide defect passivation step.