  The theory of the strong interaction, Quantum Chromodynamics (QCD), describes
the generation of hadronic masses and the state of hadronic matter during the
early stages of the evolution of the universe. As a complement, experiments
with ultracold fermionic atoms provide a clean environment to benchmark our
understanding of dynamical formation of condensates and the generation of bound
states in strongly interacting many-body systems.
  Renormalization group (RG) techniques offer great potential for theoretical
advances in both hot and dense QCD as well as many-body physics, but their
connections have not yet been investigated in great detail. We aim to take a
further step to bridge this gap. A cross-fertilization is indeed promising
since it may eventually provide us with an ab-initio description of
hadronization, condensation, and bound-state formation in strongly interacting
theories. After giving a thorough introduction to the derivation and analysis
of fermionic RG flows, we give an introductory review of our present
understanding of universal long-range behavior in various different theories,
ranging from non-relativistic many-body problems to relativistic gauge
theories, with an emphasis on scaling behavior of physical observables close to
quantum phase transitions (i. e. phase transitions at zero temperature) as well
as thermal phase transitions.
