In this talk, I will first give a introductive view about the works in graph signal processing, that means the studies of data or signals which are indexed by the nodes of a graph. This situation can appear for instance in the study of sensor networks, of social networks, of irregular images of images by 3D point clouds and also in many problems of graph-based data classification. In the recent years, several paths to study data on graphs where proposed and I will review the ones that amount to develop an analogy for defining a Fourier transform (and more general operators or transforms) for signals on a graph. After that, I will develop some more two examples in graph signal processing: 1) our recently proposed a framework to define filterbanks on a graph that is based on a partition of this graph in a set of connected sub-graph. In this way, we design a critically-sampled compact-support biorthogonal transform for graph signals. 2) the use of concepts of graph signal processing to develop accelerated versions of spectral clustering of data, using filtering (defined on graph) of random signals. These works were done jointly with Nicolas Tremblay (équipe PANAMA, IRISA, Inria Rennes ; soon at CNRS, GIPSA-lab, Grenoble)