Recent results for the
cross section of electron-positron annihilation into hadrons and for the
decay rates of the $Z$ boson and the $\tau$ lepton into hadrons including
corrections of order $\alpha_s^4$ are reviewed.
The consistency between two values of $\alpha_s$ measured
at vastly different energies constitutes
a striking test of asymptotic freedom and requires the proper matching
conditions
at charm and bottom thresholds.
Combining the results from $Z$ and $\tau$ decays
leads to $\alpha_s(M_Z)=0.1198 \pm 0.0015$ as one of the most precise and
presently only
NNNLO result for the strong coupling constant. We report a recent
determination of $\alpha_s$
which is based on a lattice evaluation of the pseudoscalar correlator for
the charm quarks combined
with continuum perturbation theory.
