The short-time Fourier transform is an important tool for signal processing (even in the background of MP3) but also for time-frequency analysis. Suitably normalized it is an isometric embedding from L2(R) (the space of ``finite energy signals'') into a subspace of L2(R2), consisting of certain continuous and square integrable functions over the time-frequency plane. Hence one finds an inversion formula, allowing to write any f in L2(R) as a superposition of time-frequency shifted copies of a given atom. According to the suggestion of D.Gabor (1946) one should use as ``atom'' a Gauss function (for optimal concentration in time and frequency), and obtain a unique expansion of L2-functions from such a system. Equivalently, one can recover a signal f from samples over the lattice aZ x bZ, for a = 1 = b. It turns out that this is not true, but only for ab < 1 (and certainly not for ab > 1). Unlike the case of the continuous wavelet transform, where a good choice of the mother wavelet allows to obtain very nice orthonormal systems, the Balian-Low theorem prohibits the existence of nice Gaborian orthonormal basis for L2(R). Some general results about Gabor frames and perhaps Gabor multipliers will be briefly mentioned.