  We review the status of the searches for the Higgs boson in the context of
the Standard Model and the Minimal SuperSymmetric Standard Model by the CDF and
DO experiments at the Fermilab Tevatron proton-antiproton collider, using up to
$2.4 \rm{fb}^{-1}$ of Run II data. Since no evidence of signal above the
expected background is observed in any of the various final states examined,
limits at 95% confidence level are presented.
