Capturing an accurate view of the Internet topology is of great interest to the networking research community as it has many uses ranging from the design and evaluation of new protocols to the vulnerability analysis of Internet infrastructure. The scale of the Internet topology coupled with its distributed and heterogeneous nature makes it very challenging to capture a complete and accurate snapshot of the topology.

In this report, we survey some of the main research studies on the discovery and characterization of the Internet topology during the past 15 years. Toward this end, we classify prior studies based on the "resolution" of the topology that they have considered as follows: interface-level, router-level, PoP-level and AS-level. For studies related to each resolution, we examine techniques and tools for data collection along with their limitations and summarize their key findings. We also discuss modeling efforts and geographic characteristics for studies at certain resolution. Our structured examination of prior research on Internet topology also reveals some exciting research problems in this area that deserve further investigation.