In contrast with the central arguments of the event structure, which have been extensively studied, much less attention has been given to non-arguments. To bridge this gap, the present volume focuses on prepositional and adverbial phrases expressing instrumental, causal, spatial, temporal roles and the like, i.e. semantic roles which have been typically associated with oblique case. The various contributions show that case in general, and oblique case in particular, is at the intersection between form and meaning: at issue are the nuclear versus non-nuclear status of these phrases and the semantic roles they express. The import of these phrases on the event structure is described in a functional-cognitive perspective for Cora, Nyulnyul, German, Dutch, French and Spanish.The specific analyses of empirical phenomena presented in this volume, as well as their implications for linguistic theory in general, will be of interest for scholars interested in syntax, semantics and pragmatics.This is the sixth and final volume of the Case and Grammatical Relations across Languages project.