  A brief review of the problem of the determination of light-quark masses from
QCD sum rules for the correlators of scalar and pseudoscalar currents is given.
Special attention is paid to the description of the large-$N_f$ results,
obtained in collaboration with Broadhurst and Maxwell, for the scalar
correlator, and estimates of its higher-order perturbative uncertainties within
the renormalon-inspired large-$\beta_0$ expansion in the $\overline{\rm MS}$
scheme are given. Brief discussion is presented of the results of calculations
of higher-order perturbative QCD corrections to the relation between pole and
$\overline{\rm MS}$-scheme running-quark masses. Their comparison with the
different estimates is also given.
