  The strong coupling constant alpha_s(mu_0), taken at a fixed reference scale
mu_0, is the single free parameter of QCD and should be known to the highest
available precision. The value of alpha_s should also be determined with good
accuracy over as large a range of scales as possible, in order to reveal
potential anomalous running in the strength of the strong interaction. Lattice
QCD is now able to calculate alpha_s with accuracy comparable to or better than
experiment. We review the status of such lattice calculations in quenched and
full QCD.
