Uses
Monads are used in functional programming to express types of sequential computation (sometimes with side-effects). See monads in functional programming, and the more mathematically oriented Wikibook module b:Haskell/Category_theory.
In categorical logic, an analogy has been drawn between the monad-comonad theory, and modal logic via closure operators, interior algebras, and their relation to models of S4 and Intuitionistic logics.
Read more about this topic: Monad (category Theory)