What features of brain processing and neural development support linguistic and cognitive development in young children? To what extent are the profile and timing of development in young children determined by a preordained genetic programme? Does the environment play a crucial role in determining the patterns of change observed in children growing up? These questions have been of central concern to developmental psychologists for well over a century. Yet none of them have received answers that are generally accepted by the profession. This article reviews some recent computational modelling of developmental change in children that promises to contribute to a deeper understanding of the issues behind these questions. The modelling work exploits artificial neural networks that mimic some of the basic properties of neural processing in the brain. These networks involve densely connected webs of simple processing units that propagate and transform complex patterns of activity. When exposed to a training environment, they undergo a process of self-organisation, yielding information processing systems that support new forms of behaviour. The study of the dynamics of these systems and their learning capabilities promises to provide us with important clues as to the nature of the mechanisms underlying development in infants and young children.