  The application of renormalization group techniques to bound states in
non-relativistic QED and QCD is discussed. For QED bound states like Hydrogen
and positronium, the renormalization group allows large logarithms of the
velocity, ln v (or equivalently ln alpha's), to be predicted in a universal and
simple way. The series of (alpha ln alpha)'s are shown to terminate after a few
terms. For QCD one can systematically sum infinite series of the form [alpha_s
ln alpha_s]^k$, and answer definitively the question ``alpha_s at what
scale?''.
