  Theories with varying gravitational constant $G$ have been studied since long
time ago. Among them, the most promising candidates as alternatives of the
standard General Relativity are known as scalar-tensor theories. They provide
consistent descriptions of the observed universe and arise as the low energy
limit of several pictures of unified interactions. Therefore, an increasing
interest on the astrophysical consequences of such theories has been sparked
over the last few years. In this essay we comment on two methodological
approaches to study evolution of astrophysical objects within a varying-$G$
theory, and the particular results we have obtained for boson and white dwarf
stars.
