This paper uses examples of conversational understandings, misunderstandings and non-understandings to explore the role of prototypes and schemata in conversational understanding. An investigation of the procedures by which we make sense of lexical items in utterances by fitting prototypes into schemata is followed by an examination of how schemata are instantiated across conversational sequences by means of topics. In interaction, conflicts over meaning illuminate the decisive role of social and cultural factors in understanding. Overall, understanding is seen to be critically dependent on principles of categorisation and contrast, which form the basis of both cognitive and sociocultural means of organisation.