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 4.3 fb{sup -1} of integrated luminosity in the electron decay channel with a data set of 1.68 x 10{sup 8} W candidates. The value of the W boson mass measured by D0 is M{sub W} = 80.375 {+-} 0.023 GeV when combined with the previously analyzed 1 fb{sup -1} of integrated luminosity. The CDF measurement uses 2.2 fb{sup -1} of integrated luminosity in both electron and muon decay channels with a total of 1.1 x 10{sup 8} W candidates. The value of the W boson mass measured by CDF is M{sub W} = 80.387 {+-} 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{sub W} = 80.385 {+-} 0.015GeV. I discuss the implications of the new measurement to the indirect measurement of the Standard Model Higgs boson mass.