  We present the result of searches for a low mass Standard Model Higgs boson
produced in association with a $W$ or a $Z$ boson at a center-of-mass energy of
$\sqrt{s}=$1.96 TeV with the CDF and D0 detectors at the Fermilab Tevatron
collider. The search is performed in events containing one or two $b$ tagged
jets in association with either two leptons, or one lepton and an imbalance in
transverse energy, or simply a large imbalance in transverse energy. Datasets
corresponding to up to 8.5 fb$^{-1}$ of integrated luminosity are considered in
the analyses. These are the most powerful channels in the search for a low mass
Higgs boson at the Tevatron. Recent sensitivity improvements are discussed. For
a Higgs mass of 115 \gevcc, the expected sensitivity for the most sensitive
individual analyses reaches 2.3 times the SM prediction at 95% confidence level
(C.L.), with all limits below 5 times the SM. Additionally, a $WZ/ZZ$
cross-section measurement is performed to validate the analysis techniques
deployed for searching for the Higgs.
