This chapter takes note of the longstanding orientation Systemic Functional Linguistics (SFL) to discourse studies before moving to a more detailed and selective presentation of current developments in SFL with respect to discourse models, developing research methodologies, and applications to different domains. The reinterpretation of cohesion as discourse semantics (identification, negotiation, conjunction, and ideation) is reviewed with respect to metafunctions (textual, interpersonal, and ideational). This work on texture is then related to social context through the register variables tenor, field and mode alongside genre. The chapter then reviews recent SFL-inspired research that applies these models to analysis of discourse across languages, modalities of communication, and domains. Work done on school and workplace discourse has raised new questions about appropriate units of discourse structure and their relationship to register analysis. It is predicted that some of these questions may be answered by the development of improved software for discourse analyses affording greater specificity in mapping the relationships among genres.