In this talk, I will argue that conversational language is and should be the object of study for research on language processing, given the central role that conversation likely played in the language evolution, its role in children's language acquisition, and in day-to-day life. Given this starting point, it becomes essential to understand how language is processed in conversation, in order to be able to extend models of language processing to this most central case. One feature of conversational settings is that one's conversational partner plays a key role in determining the form and content of speech. I compare the conversational partner to other types of contextual cues and discuss how partners-as-contexts are encoded in memory and how these representations guide on-line processing. In doing so, I will discuss several lines of research examining partner-specificity in the on-line accommodation of regional accents and in the use of common ground in the on-line processing of conversation. Complementary studies use a neuropsychological approach to identify the memory representations underlying these processes. These experiments examine how partner-specificity affected in the face of severe declarative memory impairments (hippocampal amnesia). The results of this research inform our understanding of how the most basic form of language use'interactive conversation'is readily tailored to different individuals, as it is processed in real time. By comparing the performance of individuals with severe declarative memory impairment with healthy matched comparisons, we are able to expand our understanding of the memory systems that encode and support these processes, as well as test long-standing claims of the dependence of partner-specific representations on declarative memory.