Systemic Functional Linguistics has had a long history of interaction with Computational Linguistics. In this chapter we address the current state of the art in attempts to apply systemic-functional linguistic models in computational contexts. The chapter focuses on the computational tasks of parsing, an area that has proved particularly resistant to systemic-functional approaches in the past, dialogue systems, and multimodality. Parsing is an essential prerequisite for many tasks of relevance to the linguist, such as corpus studies. Recent advances in human–machine interaction also emphasize the increasing relevance of dialogue systems, while all interaction and communicative artifacts are nowadays increasingly multimodal. The chapter concludes with a discussion of the value of combining computational and ystemic-functional linguistic accounts for both theory and practice, and sets out some directions for future developments.