I show how to use the "relative weights" method to extract the effective 
Polyakov line action corresponding
to SU(3) gauge theories, in particular pure-gauge, gauge-Higgs, and 
heavy quark theories.  For gauge fields
coupled to matter at finite density, the application is to the sign 
problem.  There are several techniques to
deal with the sign problem in the effective theory, and I will 
illustrate qualitative features of the solution
using mean field methods.