  We present a concise description of the basic features of gravity-matter
models based on the formalism of non-canonical spacetime volume-forms in its
two versions: the method of non-Riemannian volume-forms (metric-independent
covariant volume elements) and the dynamical spacetime formalism. Among the
principal outcomes we briefly discuss: (i) quintessential universe evolution
with a gravity-"inflaton"-assisted suppression in the "early" universe and,
respectively, dynamical generation in the "late" universe of Higgs spontaneous
electroweak gauge symmetry breaking; (ii) unified description of dark energy
and dark matter as manifestations of a single material entity - a second scalar
field "darkon"; (iii)unification of dark energy and dark matter with diffusive
interaction among them; (iv) explicit derivation of a stable "emergent
universe" solution, i.e., a creation without Big Bang; (v) mechanism for
suppression of 5-th force without fine-tuning.
