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

Conformality at large number of fermion flavors and composite Higgs