  We survey and explain some recent work at the intersection of model theory
and bimeromorphic geometry (classification of compact complex manifolds).
Included here are the essential saturation of the many sorted structure
$\mathcal{C}$ of compact Kaehler manifolds, the conjectural role of
hyperkaehler manifolds in the description of strongly minimal sets in
$\mathcal{C}$ and Campana's work on the isotriviality of hyperkaehler families
and its connection with the nonmultidimensionality conjecture.
