For a Higgs bundle over a compact Riemann surface, the Hitchin-Kobayashi correspondence says the existence of a harmonic metric is equivalent to the polystability of the Higgs bundle.  In this talk, we discuss some recent progress on the existence and uniqueness of harmonic metrics on Higgs bundles in the Hitchin section over general non-compact Riemann surfaces.  This is joint work with Takuro Mochizuki.