Abstract: During the XX century many techniques of Fourier analysis have been generalized to groups that may or may not be abelian, leading to notions of group Fourier transforms, noncommutative dualities, and abstract wavelet transforms associated to unitary group representations. These results have proved to be interesting not only from the theoretical point of view, but also for applications that range from the nowadays well-known setting of signal processing, to more recent mathematical modelling of brain's sensory areas, and vision in particular, to the contemporary development of neural networks. This talk aims to provide a nontechnical review of some theoretical aspects as well as some of the mentioned applications of the so-called abstract harmonic analysis, including works in collaboration with E. Hernández from UAM and C. Cabrelli, U. Molter, V. Paternostro from UBA.