It is well known that the canonical dual frames of Gabor frames MmbTnag, m, n∈ Z and frames of translates Tkϕ: k∈ Z , where g,ϕ∈L2(R)a,b>0,Txf(y)=f(y-x),Mxf(y)=e2πixyf(y), possess similar structure. But this is not true in general in the case of a wavelet frame. It has been a long standing problem to obtain a necessary and sufficient condition under which the canonical dual or any other dual of a wavelet frame has the wavelet structure. Until now, the problem still remains open. In this article, we give a short survey of some of the reported research towards this problem. © 2018, Forum D'Analystes, Chennai.