There is an increasing interest in developing learning analytic techniques for the analysis, and support of, high-quality learning discourse. This paper maps the terrain of discourse-centric learning analytics (DCLA), outlining the distinctive contribution of DCLA and outlining a definition for the field moving forwards. It is our claim that DCLA provides the opportunity to explore the ways in which discourse of various forms both resources and evidences learning; the ways in which small and large groups, and individuals, make and share meaning together through their language use; and the particular types of language--from discipline specific, to argumentative and socio- emotional--associated with positive learning outcomes. DCLA is thus not merely a computational aid to help detect or evidence "good" and "bad" performance (the focus of many kinds of analytics), but a tool to help investigate questions of interest to researchers, practitioners, and ultimately learners. The paper ends with three core issues for DCLA researchers--the challenge of context in relation to DCLA; the various systems required for DCLA to be effective; and the means through which DCLA might be delivered for maximum impact at the micro (e.g., learner), meso (e.g., school), and macro (e.g., government) levels.