Historical linguists have always been interested in grouping varieties and languages together into subgroups and families. However, their methodologies for doing so, and for representing the results, have until relatively recently been limited to the Comparative Method and the family tree. Criteria for family membership have rarely been formalized, while tree diagrams run the risk of factoring out important relationships reflecting language contact. Over the past 20 years, quantitative methods for comparing language data and programs for generating many trees and selecting the best, as well as alternative representations like networks, have become available. These are often borrowed from other disciplines like population biology, and offer scope for comparison with data from other domains, including genetics, archaeology and anthropology. This article reviews current and developing methodologies and debates in this emerging interdisciplinary field.