Discovery of a network topology is a challenging task. Available algorithms that rely on simple hop-limited, traceroute-style probes give different performance in terms of the completeness (fuzziness) of the resulting map, the speed of mapping, and the efficiency of mapping. In this paper, the authors provide a brief of the types of mapping abstractions that have been used and review available techniques for generating maps of the Internet's infrastructure. A small study conducted in order to compare two of these techniques is described. Results of this study indicate that informed random address probing offers more complete network maps quickly and more efficiently. They also suggest that probing from multiple sources and amalgamating the results may improve the completeness of maps.