This talk will present new multi-dimensional transformations which generalize shearlet transforms both anisotropically and isotropically to $L^2(\mathbb{R}^d)$. This is achieved by means of explicit constructions of families of reproducing Lie subgroups of the symplectic groups. The properties of these new families will be discussed. In particular, an analog of the Calder\'{o}n admissibility condition will be provided as well as a discussion of the related co-orbit space theory. Furthermore, brand new results which use the isotropic transform to create a "shearlet version" of well-known results relating to Hardy and Bergman spaces will be presented.