Children's understanding of the implications of conversation can influence their responses on tasks designed to measure conceptual development. These responses are in keeping with developmental changes in the ability to recognize and resolve ambiguity in communicative contexts, as shown, for example, in children's ability to compute "scalar implicatures". Examining steps children take to overcome difficulties in processing the relevant features of tasks and in correctly interpreting task instructions promise to illuminate mechanisms of conceptual development. We review recent research in this area, focussing on early knowledge of the appearance-reality distinction and knowledge of cosmological concepts.