  We determine central charges, critical exponents and appropriate gradient
flow relations for nonsupersymmetric vector-like and chiral Gauge-Yukawa
theories that are fundamental according to Wilson and that feature calculable
UV or IR interacting fixed points. We further uncover relations and identities
among the various local and global conformal data. This information is used to
provide the first extensive characterisation of general classes of free and
safe quantum field theories of either chiral or vector-like nature via their
conformal data. Using large $N_f$ techniques we also provide examples in which
the safe fixed point is nonperturbative but for which conformal perturbation
theory can be used to determine the global variation of the $a$ central charge.
