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The title of my talk pointed out central statements: the impact ofnon-perturbative QCD on {\bf CP} asymmetries in many-body FS in charm \& beautyhadrons. For practical reasons one measures first {\bf CP} violation intwo-body final states of heavy flavor hadrons. However, those are small partsof charm hadrons and tiny ones for beauty hadrons; therefore one has to probe{\bf CP} asymmetries in three- \& four-body final states. Thus the transitionsto the many-body FS basically give information about the underlying dynamics.The impact of non-perturbative QCD on {\bf CP} asymmetries in many-body FSshows that -- in principle; it is a true challenge even in a semi-quantitativeway. One needs correlations with other transitions. That is my strategy;however, I have to discuss the tactics on the same level like using consistentparameterization of the CKM matrix. Our community has entered a novel era:direct {\bf CP} violation has been found in $D^0 \to h^+h^-$ decays\cite{CHARM}. Finally I give short comments about the possible impact of NewDynamics on direct {\bf CP} violation in $K_L \to 2 \pi$ and probe {\bf CP}asymmetry in $J/\psi \to \bar \Lambda \Lambda$ transitions.

Impact of Non-perturbative QCD on CP Violation in Many-Body Final States of Flavor Transitions