The inference of the evolutionary history of a set of languages is a complex problem. Although some languages are known to be related through descent from common ancestral languages, for other languages determining whether such a relationship holds is itself a difficult problem. In this paper we report on new methods, developed by linguists Johanna Nichols (Berkeley), Donald Ringe (Penn), and Ann Taylor (Penn), and computer scientist Tandy Warnow (Penn), for answering some of the most difficult questions in this domain. These methods and the results of the analyses based upon these methods were presented in November 1995 at the Symposium on the Frontiers of Science of the National Academy of Science.