  We review the formalism of the effective average action in quantum field
theory which corresponds to a coarse grained free energy in statistical
mechanics. The associated exact renormalization group equation and possible
nonperturbative approximations for its solution are discussed. This is applied
to QCD where one observes the consecutive emergence of mesonic bound states and
spontaneous chiral symmetry breaking as the coarse graining scale is lowered.
We finally present a study of the chiral phase transition in two flavor QCD. A
precision estimate of the universal critical equation of state for the
three-dimensional O(4) Heisenberg model is presented. We explicitly connect the
O(4) universal behavior near the critical temperature and zero quark mass with
the physics at zero temperature and a realistic pion mass. For realistic quark
masses the pion correlation length near $T_c$ turns out to be smaller than its
zero temperature value.
