Final achievements on Higgs boson searches at the LEP collider

The Higgs boson searches in e+e- collisions at LEP are reviewed and the results as of September 2002 are presented. The phenomenology of the Higgs boson decays in the Standard Model (SM) as well as in various models beyond that, is outlined. The results reported in this article are obtained including all the data recorded by the LEP collider at centre-of-mass energies up to 209 GeV, but in most searches (unless stated otherwise), the final numbers are still to come. 17 Refs.