  Electroweak radiative corrections will play a major role in the analysis of
several upcoming ultra-precision experiments such as Belle-II, so is crucial to
make sure that they are fully under control. The article outlines the recent
developments in the theoretical and computational approaches to one-loop (NLO)
electroweak radiative corrections to the parity-violating asymmetry in $e^- e^+
\to \mu^- \mu^+ (\gamma)$ process with longitudinally polarized electrons. We
derive asymptotic expressions for low and high energy regions (well below or
above $Z$-resonance, correspondingly) and analyze the leading contributions.
For most of energy regions, our results are in good agreement with precise
computer-algebra based calculation and can used as a quicker alternative.
