In this talk, we present recent developments concerning frames as systems of iterations, which arise from the so called " dynamical sampling problem". In dynamical sampling, an unknown function and its future states are coarsely sampled at several time instances. The goal is to recover the unknown function from these space-time samples.

Frames as systems of iterations are generated by iterative actions of a bounded linear operator A on a countable set of vectors G in a separable Hilbert space H. We study their properties such as scalability and stability.