Wavelets and fractals share the feature of ``scaling''. Groupoids help to clarify this feature and help to reveal the interconnections among the constructs used to build fractals and wavelets. In this talk, we want to discuss which aspects of wavelet theory are intrinsic to the underlying geometry of the situations under consideration and which are artifacts of special representations. We want to identify, in terms of groupoids, the key parameters used to construct wavelets and to identify their degrees of freedom.