  The study of sampling signals on graphs, with the goal of building an analog
of sampling for standard signals in the time and spatial domains, has attracted
considerable attention recently. Beyond adding to the growing theory on graph
signal processing (GSP), sampling on graphs has various promising applications.
In this article, we review current progress on sampling over graphs focusing on
theory and potential applications. Although most methodologies used in graph
signal sampling are designed to parallel those used in sampling for standard
signals, sampling theory for graph signals significantly differs from the
theory of Shannon--Nyquist and shift-invariant sampling. This is due in part to
the fact that the definitions of several important properties, such as shift
invariance and bandlimitedness, are different in GSP systems. Throughout this
review, we discuss similarities and differences between standard and graph
signal sampling and highlight open problems and challenges.
