  A review of different cosmological models in diverse dimensions leading to a
relatively small time variation of the effective gravitational constant G is
presented. Among them: 4-dimensional general scalar-tensor model,
multidimensional vacuum model with two curved Einstein spaces, multidimensional
model with multicomponent anisotropic "perfect fluid", S-brane model with
scalar fields and two form field etc. It is shown that there exist different
possible ways of explanation of relatively small time variation of the
effective gravitational constant G compatible with present cosmological data
(e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional
cosmological models with different matter sources. The experimental bounds on
G-dot may be satisfied ether in some restricted interval or for all allowed
values of the synchronous time variable.

General Relativity and Quantum Cosmology