Recent years have witnessed an explosion of interest to the problem of Big Data. At its core, Big Data requires innovative techniques for representation, learning, and processing of massive datasets that arise in very different contexts, including social and economic networks, internet, image and video databases, sensor and transportation networks, molecular and gene interactions. It has become common to represent the structure of these datasets, such as similarities and dependencies between data elements or interactions between individuals in social networks, using graphs. Most existing techniques for learning and processing of structured data, however, resort to studying the graphs representing the structure rather that the datasets themself. In this talk, we discuss a framework for the analysis of structured data that is inspired by, and is an extension of, the traditional signal processing theory. We show that many fundamental signal processing concepts, such as filtering, spectrum, and Fourier transform, can be defined for structured datasets and applied to various problems in data learning and analysis.