The paper examines variation in the interpretations of imperfectives in Slavic, Romance, and Jê (Mẽbengokre). It develops a core modal analysis for an imperfective operator (IMPF) within situation semantics, coupled with languagespecific constraints formally encoded in modal bases. Cross-linguistic contrasts in the interpretation of imperfectives are explained in terms of variation in modal bases for IMPF, lexicalization patterns, and its interactions with other operators. The proposal accounts for why Romance languages use imperfectives to make reference to past plans while most Slavic languages do not, as well as for narrative uses specific to Romance languages, and factual uses specific to some Slavic languages. The proposal also accounts for lexically specified aspectual operators in Mẽbengokre, as well as language-specific interaction between IMPF and other modal operators, as in the Bulgarian Renarrated Mood, and two different semantic instances of Slavic Involuntary States. Appealing to cross-linguistic evidence to argue for a view according to which IMPF makes significant semantic contributions in all occurrences, the paper shows how a modal analysis can account for well-known temporal properties of imperfectives. It also demonstrates that data from closely related as well as unrelated languages provide evidence for an invariant semantic core behind imperfectivity.