  I describe results on screening masses in hot gauge theories. Wilsonian
effective long distance theories called dimensionally reduced (DR) theories
describe very well the longest screening length in pure gauge theories. In the
presence of fermions, meson-like screening lengths dominate the long-distance
physics for 3T_c/2 < T < 3 T_c, and thus obstruct perturbative DR.
Extrapolation of our results indicates that a form of this obstruction may
remain till temperatures of 10 T_c or higher, and therefore affect the entire
range of temperature expected to be reached even at the Large Hadron Collider.
