Recent progress on QCD sum rule determinations of the light and heavy quark
masses is reported. In the light quark sector a major breakthrough has been
made recently in connection with the historical systematic uncertainties due to
a lack of experimental information on the pseudoscalar resonance spectral
functions. It is now possible to suppress this contribution to the 1% level by
using suitable integration kernels in Finite Energy QCD sum rules. This allows
to determine the up-, down-, and strange-quark masses with an unprecedented
precision of some 8-10%. Further reduction of this uncertainty will be possible
with improved accuracy in the strong coupling, now the main source of error. In
the heavy quark sector, the availability of experimental data in the vector
channel, and the use of suitable multipurpose integration kernels allows to
increase the accuracy of the charm- and bottom-quarks masses to the 1% level.Comment: Invited review paper to be published in Modern Physics Letters
