In this talk we will consider two kinds of modal expansions of t-norm based fuzzy logics. The first kind follow from generalizing Kripke frames where models, with many-valued worlds and accessibility relations. We will overview current state of the art, with axiomatisations and complexity issues where available. The second kind of formalisms have appeared as simpler (non-nested fragments) but flexible enough logics to reason with graded notions of uncertainty (probability, possibility), preference of similarity, even when applied to many-valued or fuzzy events. We will exemplify the use of both kinds of modal logics to define a logic for belief functions on mv-algebras of events.

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