This thesis investigates the syntax of so-called ‘dative’ arguments in Greek and the role of their abstract Case feature in their licensing, from a generative/minimalist perspective. The main claim of the thesis is that dative arguments of all types originate low, i.e. within the maximal projection of the root, in accordance with universal linking principles, and that all apparent variation regarding their realisation and their A-/A’- behaviour can be parameterised in terms of their Case feature and the way it is valued. The secondary claims/premises on which the main claim depends are: (a) a distinction between syntactically inactive and active inherent Case features, which are both possible for dative argument DPs, with purely structural Case being a third possibility cross-linguistically attested; (b) the assumption that minimality effects in phi-Agree must be relativised to Case features; (c) a movement analysis of dative shift; (d) a novel view of applicatives as elements that simply attract dative arguments to their specifier for Case-related reasons, rather than introducing/selecting them. On this view, applicatives are last resort elements and their possible heights of attachment are derivable from the event structure of the predicate. This theory of Appl attachment, coupled with a thematic hierarchy that distinguishes goals from non-goals (and experiencers) with respect to their base position derives the full typology of dative arguments. In support of these assumptions, this thesis draws on evidence from person restrictions in transitive contexts with datives and beyond (Chapter 2), which seem to be best accounted for if the argument affected by the restriction is treated as a (defective) intervener between the dative and an applicative head; the interference of (different types of) datives themselves with agreement relations in various configurations, in Greek as well as cross-linguistically (Chapter 3); the A-/A’-properties of dative arguments of all types in Greek and Romance and novel diagnostics for unpronounced copies with syntactic or interpretive effects (Chapter 4); the diachronic and cross-dialectal behaviour of dative arguments in Greek (Chapter 5), which confirms some empirical correlations that necessitate the assumptions listed above, most notably the generalisation that both (i) the strong Person Case Constraint, and (ii) minimality effects in Agree across datives imply the availability of active Case on indirect object DPs, which is minimally manifested by the existence of the dative-shifted/double-object construction.