This paper focuses on the temporal and modal meanings associated with root infinitives (RIs) and other non-finite clauses in several typologically diverse languages--English, Russian, Greek and Dutch. I discuss the role that event structure, aspect, and modality play in the interpretation of these clauses. The basic hypothesis is that in the absence of a tense specification, the temporal reference of non-finite clauses is determined by the event structure of the predicate, in particular by the property of event closure. General principles of aspectual interpretation, such as the Punctuality Constraint (Giorgi and Pianesi 1997) and the Default Anchoring Requirement (a special case of a broader requirement that all clauses be temporally interpreted) interact with the particular aspectual features of the target language to explain the cross-linguistic differences in the temporal interpretation (past/present/modal) non-finite clauses.