Arrow is a useful typeclass for modeling something that behave like functions, e.g,. Function1: A => B, Kleisli: A => M[B] (also known as ReaderT), Cokleisli: F[A] => B, etc. So useful, that Haskell provides a proc notation for composing and combining Arrows, similar as the do notation for sequencing monadic operations. The proc notation comes in really handy, since without it, Arrows have to be used point-free, which impairs readability.
The Haskell Wikibook has a nice little example of a Hangman implementation based on an Arrow type called Circuit. Circuit is basically a fancy function which takes an A, and in addition to returning a B, it also returns a new Circuit[A, B]. This sounds similar as the State monad (which returns a result and a new State from an initial State), and indeed, Circuit can be used to perform stateful computations.
Both Scalaz and Cats provide the Arrow typeclass. I wrote a Scala implementation of Arrow Hangman using Scalaz, which closely follows the Haskell implementation, except that Scala has no proc notation (although it is possible to create one), so we resort to raw combinators like >>>, &&& and ***. It’s not too bad though, as long as we give names to intermediate steps, rather than doing all the combination in one huge expression.