The goal of this dissertation is twofold. First, we aim to identify the source of distributivity in natural language. Our hypothesis is that throughout the grammar, distributivity can be tracked down to a single operator. Two converging lines of reasoning help us identify this operator. One line emerges as a result of generalizing and unifying previously disparate treatments of distributivity in the domain of nominal quantiﬁers. The other line comes from analyzing the meaning of durative adverbials, with special attention to their interaction with cumulative readings. Second, we aim to provide a uniﬁed formal semantic framework for the treatment of interactions between verbs and their arguments, most importantly aspect, plurality, and quantiﬁcation, and to shed light on the way in which thematic arguments are associated with the verb in the lexicon and in the compositional process. Although existing frameworks deal with parts of this picture, no such uniﬁed framework exists to date. The theoretical results presented in this proposal include a novel argument in favor of a quantiﬁcational analysis of durative adverbials (Dowty, 1979; Moltmann, 1991); a novel account of cumulativity and distributivity that covers both the two-quantiﬁer and three-quantiﬁer case in the nominal domain, including readings prominently discussed by Schein (1993); a reason for severing not only the external, but also the internal argument from the semantics of the verb, in response to Kratzer (1996); and the ﬁrst event-based semantics for Tree-adjoining grammar (TAG, Joshi et al., 1975).