This paper surveys work on applying the insights of lexicalized grammars to low-level discourse, to show the value of positing an autonomous grammar for low-level discourse in which words (or idiomatic phrases) are associated with discourse-level predicate–argument structures or modification structures that convey their syntactic-semantic meaning and scope. It starts by describing a lexicalized Tree Adjoining Grammar for discourse (D-LTAG). It then reviews an initial experiment in parsing text automatically, using both a lexicalized TAG and D-LTAG, and then touches upon issues involved in how lexico-syntactic elements contribute to discourse semantics. The paper concludes with a brief description of the Penn Discourse TreeBank, a resource being developed for the study of discourse structure and semantics.