The last decade has seen an upsurge of interest in the question of language evolution within the broader area of the evolution of the human mind. It has been a multidisciplinary effort, but resorting to computational modelling to constrain and simulate the alleged dynamics of the process has been crucial for the respectability of the effort. Several formal approaches have been applied: evolutionary game theory, genetic algorithms, artificial life multiagents, connectionist simulations. In this presentation, I will introduce some of the hot issues in this area, and will focus on a particular question: whether the evolution of language involved the selection of a "language acquisition device", an innate mechanism specific for the learning of a language. It is as regards this question that the computational models have proved most critical: I will review some of the relevant contributions in this respect.