Gelfand triples are established from three spaces, a (small) Banach space, its (large) dual space, with a natural embedding of the small one into the large one, and "in between" a Hilbert space. These three topologies, three norm topologies as well as the weak*-topology on the dual space. We will indicate in this talk that such Banach Gelfand Triples arise in many places in Harmonic analysis, and how to express familiar facts about the Fourier transform, Gabor expansions, or spline-type spaces in terms of mappings between such Gelfand triples. For example, the Fourier transform can be characterized as the unique unitary BGT-isomorphism which maps pure frequencies into Dirac measures.