Let $G$ be a complex affine reductive group and let $K$ be a maximal compact subgroup. We have recently proved that the moduli space of representations $\operatorname{Hom}(F,G)/G$ deformation retracts to the quotient space $\operatorname{Hom}(F,K)/K$ for any rank $r$ free group $F$. If $F$ is replaced by other finitely generated groups the theorem may be false, but not always. In this talk we discuss this theorem and some examples.