The topology of the Internet at the autonomous system (AS) level is not yet fully discovered despite significant research activity. The community still does not know how many links are missing, where these links are and finally, whether the missing links will change our conceptual model of the Internet topology. An accurate and complete model of the topology would be important for protocol design, performance evaluation and analyses. The goal of our work is to develop methodologies and tools to identify and validate such missing links between ASes. In this work, we develop several methods and identify a significant number of missing links, particularly of the peer-to-peer type. Interestingly, most of the missing AS links that we find exist as peer-to-peer links at the Internet exchange points (IXPs). First, in more detail, we provide a large-scale comprehensive synthesis of the available sources of information. We cross-validate and compare BGP routing tables, Internet routing registries, and traceroute data, while we extract significant new information from the less-studied Internet exchange points (IXPs). We identify 40% more edges and approximately 300% more peer-to-peer edges compared to commonly used data sets. All of these edges have been verified by either BGP tables or traceroute. Second, we identify properties of the new edges and quantify their effects on important topological properties. Given the new peer-to-peer edges, we find that for some ASes more than 50% of their paths stop going through their ISPs assuming policy-aware routing. A surprising observation is that the degree of an AS may be a poor indicator of which ASes it will peer with.