Dynamical sampling is a term describing an emerging set of problems related to recovering signals and evolution operators from space-time samples. For example, consider the abstract IVP in a separable Hilbert space $\mathcal{H}$:

where $t\in[0,\infty)$, ${u}: \mathbb{R}_+ \to \mathcal{H}$,

$\dot{u}: \mathbb{R}_+\to\mathcal{H}$ is the time derivative of $u$, and $u_0$ is an initial condition. When, $F=0$, $A$ is a known (or unknown) operator, and the goal is to recover $u_0$ from the samples $\{u(t_i,x_j)\}$ on a sampling set $\{(t_i,x_j)\}$, we get the so called {\em space-time sampling} problems. If the goal is to identify the operator $A$, or some of its characteristics, we get the {\em system identification} problems. If instead we wish to recover $F$, we get the {\em source term} problems. In this talk, I will present several results on dynamical sampling, their connection to frames and inverse problems.