Status of Higher-Order Corrections in the Standard Electroweak Theory

We review recent theoretical progress in the computation of radiative corrections beyond one loop within the standard model of electroweak interactions, both in the gauge and Higgs sectors. In the gauge sector, we discuss universal corrections of $\O(G_F^2M_H^2M_W^2)$, $\O(G_F^2m_t^4)$, $\O(\alpha_sG_FM_W^2)$, $\O(\alpha_s^2G_Fm_t^2)$, and those due to virtual $t\bar t$ threshold effects, as well as specific corrections to $\Gamma\left(Z\to b\bar b\right)$ of $\O(G_F^2m_t^4)$, $\O(\alpha_sG_Fm_t^2)$, and $\O(\alpha_s^3)$ including finite-$m_b$ effects. We also present an update of the hadronic contributions to $\Delta\alpha$. Theoretical uncertainties, other than those due to the lack of knowledge of $M_H$ and $m_t$, are estimated. In the Higgs sector, we report on the $\O(\alpha_sG_Fm_t^2)$ corrections to $\Gamma\left(H\to f\bar f\,\right)$ including those which are specific for the $b\bar b$ mode, the $\O(\alpha_s^2)$ corrections to $\Gamma\left(H\to q\bar q\right)$ including the finite-$m_q$ terms, and the $\O(\alpha_s)$ corrections to $\Gamma(H\to gg)$.