  We review and streamline our previous results and the results of Y.Ostrover
on the existence of Calabi quasi-morphisms and symplectic quasi-states on
symplectic manifolds with semi-simple quantum homology. As an illustration, we
discuss the case of symplectic toric Fano 4-manifolds. We present also new
results due to D.McDuff: she observed that for the existence of
quasi-morphisms/quasi-states it suffices to assume that the quantum homology
contains a field as a direct summand, and she showed that this weaker condition
holds true for one point blow-ups of non-uniruled symplectic manifolds.
