  The current status of determinations of the QCD running quark masses is
reviewed. Emphasis is on recent progress on analytical precision determinations
based on finite energy QCD sum rules. A critical discussion of the merits of
this approach over other alternative QCD sum rules is provided. Systematic
uncertainties from both the hadronic and the QCD sector have been recently
identified and dealt with successfully, thus leading to values of the quark
masses with unprecedented accuracy. Results currently rival in precision with
lattice QCD determinations.

High Energy Physics - Phenomenology;High Energy Physics - Lattice