  While indirect & direct CP violations (CPV) had been established in the
decays of strange & beauty mesons, none have been done for baryons. There are
different "roads" for finding CP asymmetries in the decays of strange baryons;
they are highly non-trivial ones. The HyperCP Collaboration had probed CPV in
the decays of single $\Xi$ & $\Lambda$ [Phys.Rev.Lett 93 (2004) 262001]. We
talk about future lessons from $e^+e^-$ collisions at BESIII/BEPCII: probing
decays of pairs of strange baryons, namely $\Lambda$, $\Sigma$ & $\Xi$.
Realistic goals are to learn about non-perturbative QCD. One can hope to find
CPV in the decays of strange baryons; one can also dream to find impact of New
Dynamics (ND). We point out that a new important era starts with the
BESIII/BEPCII data accumulated by the end of 2018.
