The aim of this paper is to clarify what kind of normativity characterizes a convention. First, we argue that conventions have normative consequences because they always involve a form of trust and reliance. We contend that it is by reference to a moral principle impinging on these aspects (i.e. the principle of Reliability) that interpersonal obligations and rights originate from conventional regularities. Second, we argue that the system of mutual expectations presupposed by conventions is a source of agreements. Agreements stemming from conventions are "tacit" in the sense that they are implicated by what agents do (or forbear from doing) and without that any communication between them is necessary. To justify this conclusion, we assume that: (1) there is a salient interpretation, in some contexts, of everyone's silence as confirmatory of the others' expectations (an epistemic assumption), and (2) the participating agents share a value of not being motivated by hostile attitudes (a motivational assumption). By clarifying the relation between conventions and agreements, the peculiar normativity of conventions is analyzed.