Research addressing the possible cognitive consequences of bilingualism for children’s development has found mixed results when seeking effects in domains such as language ability and intelligence. The approach in the research reported in this chapter is to investigate the effect that bilingualism might have on specific cognitive processes rather than domains of skill development. Three cognitive domains are examined: concepts of quantity, task-switching and concept formation, and theory of mind. The common finding in these disparate domains is that bilingual children are more advanced than monolinguals in solving problems requiring the inhibition of misleading information. The conclusion is that bilingualism accelerates the development of a general cognitive function concerned with attention and inhibition, and that facilitating effects of bilingualism are found on tasks and processes in which this function is most required.