According to the predictions from the Standard Model, a low mass Higgs boson decays preferentially into a pair of b-quarks. Despite large backgrounds, this decay mode has been studied both at the Tevatron and at the LHC in the associated production with a weak vector boson (W/Z). This has been done in the following channels: W(μν)H, W(eν)H, Z(μμ)H, Z(ee)H and Z(νν)H. We will discuss the most recent analyses published by the ATLAS, CDF, CMS and D0 collaborations and recent progress in b-jet identification, analysis techniques (including the use of MVA tools) and the crucial aspects of validating both the background description in the signal region and the strategies employed. Finally, the most recent upper limits on the VH production cross section times the H to bb branching ratio, with respect to the expectations for a Standard Model Higgs boson, will be presented.