Recent reanalyses of the atomic physics effects on the weak charge in cesium have led to a value in much closer agreement with predictions of the Standard Model. We review precision electroweak tests, their implications for upper bounds on the mass of the Higgs boson, possible ways in which these bounds may be circumvented, and the requirements placed upon accuracy of future atomic parity violation experiments by these considerations. [3,5]) with this property have been constructed. Other related discussions may be found in [6,7,8].Among the electroweak observables that play a role in precise tests of the radiative corrections in the theory, atomic parity violation plays a special role. Many types of new physics affect what are known as "oblique corrections," through vacuum polarization of the photon, Z, and W bosons. These effects have been described by Peskin and Takeuchi [9] in terms of two parameters S and T , upon which various observables depend linearly, with S = T = 0 corresponding to "no new physics," given nominal values of the top quark and Higgs boson masses. The weak charge Q W measured in parity-violation experiments in such atoms as cesium [10, 11], bismuth [12], lead [13], and thallium [14,15] is mainly sensitive to the variable S, with very small dependence on T [16, 17, 18]. Thus, atomic parity violation experiments can shed unique light on certain types of new physics which contribute to the parameter S [19,20,21].Atomic physics calculations have been carried out for such systems as cesium [22] and thallium [23]. In 1999 the JILA-Boulder group reported measurements in cesium [11] that reduced uncertainties in previous calculations. This led to a resulting weak charge, Q W (Cs) = −72.06 ± 0.28 expt ± 0.34 theor = −72.06 ± 0.46 which represented a