Abstract. Since the nineties, the Internet has seen an impressive growth, in terms of users, intermediate systems (such as routers), autonomous systems, or applications. In parallel to this growth, the research commu-nity has been looking for obtaining and modeling the Internet topology, i.e., how the various elements of the network interconnect between them-selves. An impressive amount of work has been done regarding how to collect data and how to analyse and model it. This chapter reviews main approaches for gathering Internet topology data. We first focus on hop limited probing, i.e., traceroute-like prob-ing. We review large-scale tracerouting projects and discuss traceroute limitations and how they are mitigated by new techniques or extensions. Hop limited probing can reveal an IP interface vision of the Internet. We next focus on techniques for aggregating several IP interfaces of a given router into a single identifier. This leads to a router level vision of the topology. The aggregation can be done through a process called alias resolution. We also review a technique based on IGMP probing that silently collect all multicast interfaces of a router into a single probe. We next refine the router level topology by adding subnet information. We finish this chapter by discussing the AS level topology, in particular the relationships between ASes and the induced hierarchy.

Internet topology research is concerned with the study of the various types of connectivity structures that are enabled by the layered architecture of the Internet. More than a decade of Internet topology research has produced a number of high-profile "discoveries " that continue to fascinate the scientific community, even though (or, especially because) they have been simultaneously touted by different