The present upgrades of the CDF and D0 detectors as well as of
the Fermilab Tevatron have dramatically improved their sensitivity for
Standard Model and minimal supersymmetry Higgs boson searches in Run II.
This paper reviews the recent estimates of this sensitivity in terms of
Higgs discovery and exclusion reach based on a total expected Run II
Tevatron luminosity of 15 fb-1 delivered to each experiment.