At the end of the 18th century Prony discovered that an s-sparse d-dimensional vector can be recovered from 2s of its consecutive Fourier coefficients. This result has seen numerous generalizations and appears in various other contexts. For example, it is useful for understanding concepts such as compressed sensing, super-resolution, and uncertainty principles. In this talk, I will describe a relatively novel approach which regards Prony’s problem as a spectral identification problem for an unknown restriction of a known linear operator. We will see that a Prony-type method applies in a very general context of Banach modules and may be used for problems such as the spectral identification in dynamical sampling and the time-varying channel identification in wireless communication. The talk is based on joint papers with A. Aldroubi and G. Pfander.