Conversational exchanges have unique properties that have a great potential for language acquisition such as the motivation to communicate, information about language meanings and structures, and the construction of new ways of expression. Results from the literature and from new data analyses show that conversational exchanges have both immediate and long-term effects. Two properties are considered here to have particularly great learning potential. One is the facilitated access to unities of meaning underlying the successive transformations in utterance shapes, cognitively analogous to the discovery of physical and logico-mathematical invariances under the transformations of shape and configuration. The other is the co-construction of sequences that foreshadow behaviors still beyond the individual child's present capacities.