  The framework for considering the astronomical and cosmological observations
in the context of scalar-tensor quintessence in which the quintessence field
also accounts for a time dependence of the gravitational constant is developed.
The constraints arising from nucleosynthesis, the variation of the constant,
and the post-Newtonian measurements are taken into account. A simple model of
supernovae is presented in order to extract the dependence of their light
curves with the gravitational constant; this implies a correction when fitting
the luminosity distance. The properties of perturbations as well as CMB
anisotropies are also investigated.
