Searches for the Higgs boson at the Fermilab Tevatron Collider are
described.  Results are reported from both the CDF and D0 experiments, based
on the data collected in the Run I period.  Higgs boson searched include
Standard Model, MSSM Higgs, as well as bosonic Higgs.  No signal is observed
and limits are set for production cross sections for several channels.