The Web graph, meaning the graph induced by Web pages as nodes and their hyperlinks as directed edges, has become a fascinating object of study for many people: physicists, sociologists, mathematicians, computer scientists, and information retrieval specialists.

Recent results range from theoretical (e.g.: models for the graph, semi-external algorithms), to experimental (e.g.: new insights regarding the rate of change of pages, new data on the distribution of degrees), to practical (e.g.: improvements in crawling technology).

The goal of this talk is to convey an introduction to the state of the art in this area and to sketch the current issues in collecting, representing, analyzing, and modeling this graph. Although graph analytic methods are essential tools in the Web IR arsenal, they are well known to the SIGIR community and will not be discussed here in any detail; instead, we will explore some challenges and opportunities for using IR methods and techniques in the exploration of the Web graph, in particular in dealing with legitimate and "spam" perturbations of the "natural" process of birth and death of nodes and links, and conversely, the challenges and opportunities of using graph methods in support of IR on the Web and in the enterprise.