In this paper, we will discuss the general idea of the wavelet representation, in its continuous and discrete versions, as well as in terms of a multiresolution approximation. In addition, the general expression for the affine class, and the relationship between the affine and Cohen's classes are presented. Also, the shift-scale invariant class is defined. This class basically combines the properties of both classes. Finally a recent development, namely, the use of unitary transformations in both Cohen's and the affine classes, with the consequent generation of even more specific tools for signal analysis will be discussed.