Teaching about the 'products' of science – theories, models, concepts – has been informed over recent decades by an extensive research programme originating in studies of learners' ideas in science. This 'constructivist' programme initially focused on the identification and characterisation of alternative conceptions. As the programme has progressed it has increasingly turned to exploring the origins and development of student thinking, and modelling student cognition in ways that can inform effective teaching of the target knowledge presented in the curriculum. In recent years there has been an increasing shift in the focus of science education from a preoccupation with teaching about 'products' to acknowledging that an understanding of the nature and processes of science - the provisional status of its claims; its forms of argumentation and means of producing public knowledge; and its relationship with society - is at least as significant in preparing young people for their place as consumers and voters in their own societies and as responsible global citizens in a finite world. This chapter discusses the potential of the constructivist programme to inform more effective teaching about the nature of science.