  We review the relations between compact complex manifolds carrying various
types of Hermitian metrics (K\"ahler, balanced or {\it strongly Gauduchon}) and
those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$
of the Fr\"olicher spectral sequence, as well as the behaviour of these
properties under holomorphic deformations. The emphasis will be placed on the
notion of {\it strongly Gauduchon} (sG) manifolds that we introduced recently
in the study of deformation limits of projective and Moishezon manifolds.
Various examples of sG and non-sG manifolds are exhibited while a range of
constructions already known in the literature are reviewed and reinterpreted
from this new standpoint.
