What is so special about Monads?

Question

A monad is a mathematical structure which is heavily used in (pure) functional programming, basically Haskell. However, there are many other mathematical structures available, l

Answer 1

I suspect that the disproportionately large attention given to this one particular type class (Monad) over the many others is mainly a historical fluke. People often associate IO with Monad, although the two are independently useful ideas (as are list reversal and bananas). Because IO is magical (having an implementation but no denotation) and Monad is often associated with IO, it's easy to fall into magical thinking about Monad.

(Aside: it's questionable whether IO even is a monad. Do the monad laws hold? What do the laws even mean for IO, i.e., what does equality mean? Note the problematic association with the state monad.)