Polarisation and precise calibration of the LEP beam energy

We report in this article on two issues of precision accelerator physics, performed at the LEP collider, that challenged international collaborations. The first result is an increase of the polarisation degree from an almost vanishing natural level to 50%, opening the way to energy calibration by resonant depolarisation. The second result is a systematic and precise determination of the collider centre-of- mass energy correcting for subtle effects such as the azimuthal variation of the beam energy, the magnet temperature, the effects of parasitic earth currents and terrestrial tides. It resulted in an extremely accurate test of the standard model and set significant constraints on the top quark and Higgs masses. (16 refs).