  I will review the measurements of the $b$-quark mass performed by ALEPH and
DELPHI. A large set of observables has been used together with detailed studies
on jet algorithms. Very clear effects due to the $b$-quark mass running are
observed. Comparing with the determinations at the $\Upsilon(4S)$ threshold,
the measurements of the running $b$-quark mass at the $Z$ pole are consistent
with the predicted evolution from QCD.
