Sparse representations of anisotropic structures in higher dimensions are essential in a variety of areas in applied mathematics and statistics. Although the last years have seen many new representation systems designed for this task, it was still an open problem to introduce a representation system suitable for both the analog as well as the digital world. The new representation system of shearlets satisfies all those needs. The key idea consists in parameterizing directions by slope rather than angle which is a natural fit for today's digital world. This approach allows us to provide a complete methodology to derive sparse decompositions of directional features in both the analog as well as the digital world along with a fast decomposition algorithm.