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 (p) over bar collider (root s = 1.96 TeV) by the CDF and D0 experiments with an integrated luminosity of up to 8.5 fb(-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 -> b (b) over bar decay channel (favored for M-H less than or similar to 135 GeV/c(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-H = 115 GeV/c(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(SM)(H) 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.