Let Γ be a constraint language and let I be an instance of CSP(Γ). An assignment s (of the variables of I) is a (1 − ǫ) solution, ǫ > 0, of I if it satifies at least a (1 − ǫ)-fraction of its constraints. If such an assignment exists we say that I is (1 − ǫ)-satisfiable. Let f be a real function. An f-approximation algorithm (for CSP(Γ)) is an algorithm that receives as input an instance I of CSP(Γ) and returns an assignment s, in such a way that if I is (1−ǫ)-satisfiable then s is a (1−f(ǫ))-solution. If, additionally, limǫ→0 f(ǫ) = 0 then we say that CSP(Γ) has a robust approximation algorithm. It has been conjectured by Guruswami and Zhou that CSP(Γ) has a robust approximation algorithm if and only if Γ has bounded width. In this talk we shall present some initial results towards proving this conjecture.