In this paper we present work in progress for the construction of a resource that we provisionally call Greek Dependency Treebank (GDT). Our approach involves annotation at the level of syntax and semantics and is envisioned to result in an annotated reference corpus for the Greek language, compliant with existing resources for other languages. Taking into account multi-layered annotation schemes designed to provide deeper representations of structure and meaning, we describe the methodology followed at both the syntactic and semantic layer, we report on the annotation process and the problems faced and we conclude with comments on future work and exploitation of the resulting resource.