The presentation will give some motivation for the potential of Gabor expansions of signals (which is in fact in the background of the MP3 compression scheme). In the course of the presentation, which will start from linear algebra questions, the basic algebraic, numerical and (as time permits) functional analytic questions will be touched. In particular, we will emphasize the importance of structured (Banach) frames and (Riesz) basis (of Gabor type), both from the application point and from the computational view-point.