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This is a survey of {\lambda}-calculi that, through the Curry-Howardisomorphism, correspond to constructive modal logics. We cover the prehistoryof the subject and then concentrate on the developments that took place in the1990s and early 2000s. We discuss logical aspects, modal {\lambda}-calculi, andtheir categorical semantics. The logics underlying the calculi surveyed areconstructive versions of K, K4, S4, and LTL.

The Many Worlds of Modal {\lambda}-calculi: I. Curry-Howard for Necessity, Possibility and Time