We present an overview of the analyses performed by the two experiments at the Run II of the Tevatron searching for Higgs boson production. Especial effort has been done in the search for the Higgs boson predicted by the Standard Model. The good performance of the Tevatron would allow the experiments to be sensitive to the presence of the Higgs beyond the LEP limit by the end of Run II. In addition, analyses performed in the framework of models extending the Standard Model are already covering regions not excluded by previous experiments. Results from all these analyses and plans for the future will be discussed.

PACS numbers: 14.80.Bn, 14.80.Cp