Precise measurements of the W mass at the Tevatron and indirect constraints on the Higgs mass

I describe the latest D0 and CDF W boson mass measurements. The D0 measurement is performed with $4.3f{b}^{-1}$ of integrated luminosity in the electron decay channel with a data set of $1.68\times {10}^6$ W candidates. The value of the W boson mass measured by D0 is $M_W=80.375\pm 0.023GeV$ when combined with the previously analyzed $1f{b}^{-1}$ of integrated luminosity. The CDF measurement uses $2.2f{b}^{-1}$ of integrated luminosity in both electron and muon decay channels with a total of $1.1\times {10}^6$ W candidates. The value of the W boson mass measured by CDF is $M_W = 80.387\pm 0.019, GeV$. I report the combination of these two measurements with previous Tevatron measurements and with the LEP measurements of the W boson mass. The new world average is $M_W=80.385\pm 0.015GeV$. I discuss the implications of the new measurement to the indirect measurement of the Standard Model Higgs boson mass.