One of the final hurdles for advanced L2 learners is the acquisition of lexico- and morpho-syntactic alternations when constrained by information-structure (IS) factors like topic and focus that are located at the interface of grammar and discourse. Departing from two broad research traditions in SLA (formal and functional) we review how advanced and near-native learners of different L2s deal with IS management. We discuss the reasons why they often fail to acquire the discursive nuances associated with IS-constrained phenomena like pronominal subject distribution, postverbal subjects, clefting, left dislocation, focus fronting, raising and other types of lexico-grammatical variation. We conclude by proposing that a methodological triangulation between corpus and experimental data is needed to better understand IS phenomena in L2 acquisition in the future.