This article investigates aspectual meaning and its interaction with independently motivated temporal constraints imposed by coherence relations. I argue that aspectual markers denote functions from a set of events denoted by a verb-phrase (VP) to a set of VP-event parts that are located relative to (i) an input encoding explicitly temporal information and (ii) an input encoding information about discourse connectivity. By virtue of encoding information about discourse connectivity, aspectual makers play a nontrivial role in determining which coherence relation holds between successive utterances and thereby constrain the ordering of eventualities described by these utterances. The core data that support these claims come from discourses containing the Russian imperfective. This aspect is remarkable because it can constrain the temporal location of different event parts. Depending on the event part that is constrained, the imperfective often leads to an inference that the described event precedes or overlaps a salient event previously mentioned in the discourse. I argue that the imperfective is rarely found in narrative contexts because its semantics rules the so-called OCCASION relation, which establishes a particular kind of contingency relationship between events. The proposed analysis accounts for the discourse properties of the Russian imperfective and is shown to be compatible with the modal properties of this aspect. I also show how the analysis could be extended to account for the meaning of the English progressive and temporal adverbials.