  The many open questions concerning the existence of IR and UV fixed points in
gauge theories as a function of the number of fermion flavors and bare coupling
are briefly reviewed and discussed. It is pointed out that only a small subset
of potential IR-conformal gauge theories, i.e. theories whose IR behavior is
determined by an IR fixed point, has so far been examined. It is suggested that
the naturally light scalar composites that seem to appear generically as lowest
states in the non-QCD-like spectrum of such theories provide a natural basis
for composite Higgs models, where the composite Higgs is not a NG boson and
some of the usual fine-tuning problems are evaded.
