Even though Java 8 is just a little over six years old and brought a tremendous revolution to Java, adoption of lambdas and functional approaches to programming problems is still an ongoing process.
I have introduced numerous people to functional-style programming & lambdas, and at one point came up with the idea of a small “cheat sheet” only one or two DIN A4 pages in size that you could have in hand when thinking about functional stuff. This is by no means meant to be a comprehensive introduction, but a small reference document, and has been received very well, so I thought I’d share it here.

Interface
& Method		 Type Example
Supplier<E>
E get()		 () -> E Supplier<List> factory = ArrayList::new;
stream.collect(Collectors.toList(factory));
Consumer<E>
void accept(E e)		 E -> () list.foreach(e -> e.frobnicate())
Runnable
void run()		 () -> () new Thread(() -> System.sleep(10000)).run();
Function<T,R>
R apply(T t)		 T -> R stream.map(t -> new R(t));
BiFunction<T,U,R>
R apply(T t, U u)		 (T, U) -> R stream.reduce(start, accumulator, merge)
Predicate<E>
boolean test(E e)		 E -> boolean Function<E, Boolean> but with primitive boolean

When to use

Use When Related concept
Supplier<E> If it takes nothing Factory
Consumer<E> If it returns nothing Listener, Callback
Runnable If it does neither Task
Function<F, T> If it does both Callback
BiFunction<T, U , R> If it takes two and returns one  
Predicate<E> To check semantic properties Condition

MapReduce
Important stream operations

As always, A = B is permissible!

Operation Type Input Output See also
map A -> B Stream<A> Stream<B> flatMap
filter A -> bool Stream<A> Stream<A> takeWhile
reduce (B, ((B, A) -> B), ((B, B) -> B)) -> B Stream<A> B collect is reduce

When to use

Use When
map transforming one Stream into another Stream
filter excluding elements from one stream based on a condition (predicate)
reduce making the stream “smaller” (reducing it), e.g.
- collecting multiple elements into one list
- taking a sum, maximum or minimum
- or otherwise reducing multiple elements to one element