Searches for Low Mass Higgs Boson at the Tevatron

We present the result of the searches for a low mass Standard Model Higgs boson performed at the Tevatron p{bar p} collider ({radical}s = 1.96 TeV) by the CDF and D0 experiments with an integrated luminosity of up to 8.5 fb{sup -1}. Individual searches are discussed and classified according to their sensitivity. Primary channels rely on the associate production with a vector boson (WH or ZH) and the H {yields} b{bar b} decay channel (favored for M{sub H} {approx}< 135 GeV/c{sup 2}). Event selection is based on the leptonic decay of the vector boson and the identification of b-hadron enriched jets. Each individual channel is sensitive, for M{sub H} = 115 GeV/c{sup 2}, to less than 5 times the SM expected cross section and the most sensitive channels can exclude a production cross section of 2.3 x {sigma}{sub H}{sup SM}. Secondary channels rely on a variety of final states. Although they are from 2 to 5 times less sensitive than any primary channel, they contribute to the Tevatron combination and, in some cases, they pose strong constrains on exotic Higgs boson models.