To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure router-level ISP topologies. Our techniques reduce the number of required traces compared to a brute-force, all-to-all approach by three orders of magnitude without a significant loss in accuracy. They include the use of BGP routing tables to focus the measurements, exploiting properties of IP routing to eliminate redundant measurements, better alias resolution, and the use of DNS to divide each map into POPs and backbone. We collect maps from ten diverse ISPs using our techniques, and find that our maps are substantially more complete than those of earlier Internet mapping efforts. We also report on properties of these maps, including the size of POPs, distribution of router outdegree, and the inter-domain peering structure. As part of this work, we release our maps to the community.