  We compare different non-perturbative methods for calculating the effective
action for fermionic systems featuring bosonic bound states (BBS) and
spontaneous symmetry breaking (SSB). In a purely fermionic language proceeding
into the SSB phase requires techniques beyond perturbation theory and
renormalization group equations. Improvement comes from a description with BBS
fields and elementary fields treated on equal footing. Yet, ``partial
bosonization'' introduces an arbitrariness as the choice for the composite
fields is usually not completely determined by the classical action. Results of
approximate calculations, e.g. mean field theory, may depend strongly on this
choice, thus limiting their quantitative reliability. Using the
Nambu--Jona-Lasinio model as an example we demonstrate how this dependence can
be reduced, sometimes even be eliminated by suitably chosen approximations.
  Schwinger-Dyson equations (SDE) allow for a description of SSB without
auxiliary fields. The 2PI effective action enables us to compare different
solutions of the SDE and find the stable one. We apply this method to a
six-fermion interaction resembling the three-flavor instanton interaction in
QCD. We find a first order chiral phase transition but no stable phase with
broken color symmetry.
  The existence of an elementary scalar boson in the Standard Model -- the
Higgs -- raises several questions. The smallness of its mass compared to some
fundamental scale ($\sim M_{\textrm{GUT}}$) requires an extreme amount of
fine-tuning. Moreover, its $\phi^4$-potential may not be renormalizable in a
strict sense. In view of this we discuss the possibility of a Higgs as BBS of
fermions.
