  We review the functional renormalization group (RG) approach to the BCS-BEC
crossover for an ultracold gas of fermionic atoms. Formulated in terms of a
scale-dependent effective action, the functional RG interpolates continuously
between the atomic or molecular microphysics and the macroscopic physics on
large length scales. We concentrate on the discussion of the phase diagram as a
function of the scattering length and the temperature which is a paradigm
example for the non-perturbative power of the functional RG. A systematic
derivative expansion provides for both a description of the many-body physics
and its expected universal features as well as an accurate account of the
few-body physics and the associated BEC and BCS limits.
