With the explosive growth of information and communication, signals are generated at an unprecedented rate from various sources, including social, citation, biological, and physical infrastructure, among others.

Unlike time-series signals or images, these signals possess complex, irregular structure, which requires novel processing techniques leading to the emerging field of signal processing on graphs.

Signal processing on graphs extends classical discrete signal processing to signals with an underlying complex, irregular structure. The framework models that underlying structure by a graph and signals by graph signals, generalizing concepts and tools from classical discrete signal processing to graph signal processing. I will talk about graph signal processing, and, in particular, the classical signal processing task of sampling and interpolation within the framework of signal processing on graphs. As the bridge connecting sequences and functions, classical sampling theory shows that a bandlimited function can be perfectly recovered from its sampled sequence if the sampling rate is high enough. I will follow up with a number of applications where sampling on graphs is of interest.