The central topic of this talk is the construction of Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, their construction is closely related to that of standard wavelets and Gabor systems, and they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. The construction of Gabor shearlets allows us to incorporate many desirable properties for signal analysis. This is joint work with Gitta Kutyniok (TU Berlin) and Xiaosheng Zhuang (City University of Hong Kong).