Several important recent advances in various sciences (particularly biology and physics) are based
on complex network analysis, which provides tools for characterising statistical properties of networks
and explaining how they may arise. This article examines the relevance of this trend for the study of human languages. We review some early efforts to build up language networks, characterise
their properties, and show in which direction models are being developed to explain them. These insights are relevant, both for studying fundamental unsolved puzzles in cognitive science, in particular the origins and evolution of language, but also for recent data-driven statistical
approaches to natural language.This work has been supported by grants FIS2004-0542, IST-FET ECAGENTS project of the European Community founded under EU R&D contract 011940, IST-FET DELIS project under
EU R&D contract 001907, by the Santa Fe Institute and the Sony Computer Science Laboratory.N