We critically analyse the problem of the variation of the gravitational constant with cosmological time. Since Einstein's equation does not allow G to vary on any time-scale, no observational data can be analysed within the context of the standard theory. The recently proposed scale covariant theory, which allows (but does not demand) G to vary, and which has been shown to have passed several standard cosmological tests is employed to discuss some recent non-null observational results which indicate a time variation of G.