This work is a study of the French impersonal "on" and a theory of the unique "referential deficiency" of impersonals: a range of uses that spans those covered by indefinites and definites; neutrality about content like number; systematic participation in syntactic and semantic dependencies but with unparalleled restrictions like binding of only local, number-neutral anaphora. Current understanding of the syntax and semantics of DPs and properties of French let us study this behavior in depth and extend previous findings, often in unexpected ways. The study reveals a DP with content unique in French but drawing only on options available in UG. It leads to a theory of impersonal "on" as an indefinite DP whose content interacts with certain theories of phi-features, indefinites and definites, and anaphoric dependencies to give an explanatory account of the nature of impersonals. In turn, impersonal "on" contributes to the theories that enter into its analysis: the relationship between syntactic underspecification and semantic neutrality, the nature of indefinites and their relationship to definites (Heim 1991, 2011; Heim 1982, Elbourne 2013), and minimal pronoun anaphora (Kratzer 2009). The study is extended to the grammaticalisation of a distinct 1PL "on", whose complex properties reflect the colexicalisation of impersonal "on" and a 1PL element. We end the book on the place of impersonals in the landscape of argument coding and explore the expected parameter space through "on"-like impersonals cross-linguistically. The work builds on the analysis of "on" and its kin in Cinque (1988), Chierchia (1995b), Egerland (2003b), Kayne (2010), and explores them in the Principles-and-Parameters approach to syntax and the "situated descriptions" (Elbourne 2013) extension of the syntax-semantics mapping of Heim and Kratzer (1998).