  This is a survey of {\lambda}-calculi that, through the Curry-Howard
isomorphism, correspond to constructive modal logics. We cover the prehistory
of the subject and then concentrate on the developments that took place in the
1990s and early 2000s. We discuss logical aspects, modal {\lambda}-calculi, and
their categorical semantics. The logics underlying the calculi surveyed are
constructive versions of K, K4, S4, and LTL.
