We will discuss a few ideas for sampling signals that evolve in time. The standard sampling theory is not designed to take into account the additional information provided by sampling a signal at different time levels. Using this dependency it is sometimes possible to recover the signal at a finer resolution from multiple coarse snapshots obtained at appropriate time intervals. It may also be possible to identify an unknown underlying evolution operator or its key parameters. We shall present several simple examples illustrating these ideas. The talk is based on joint work with A. Aldroubi and J. Davis.