What is the difference between def foo = {} and def foo() = {} in Scala?

If you include the parentheses in the definition you can optionally omit them when you call the method. If you omit them in the definition you can't use them when you call the method.

scala> def foo() {}
foo: ()Unit

scala> def bar {}
bar: Unit

scala> foo

scala> bar()
<console>:12: error: Unit does not take parameters
       bar()
          ^

Additionally, you can do something similar with your higher order functions:

scala> def baz(f: () => Unit) {}
baz: (f: () => Unit)Unit

scala> def bat(f: => Unit) {}
bat: (f: => Unit)Unit

scala> baz(foo)    

scala> baz(bar)
<console>:13: error: type mismatch;
 found   : Unit
 required: () => Unit
       baz(bar)
           ^
scala> bat(foo)

scala> bat(bar)  // both ok

Here baz will only take foo() and not bar. What use this is, I don't know. But it does show that the types are distinct.

Let me copy my answer I posted on a duplicated question:

A Scala 2.x method of 0-arity can be defined with or without parentheses (). This is used to signal the user that the method has some kind of side-effect (like printing out to std out or destroying data), as opposed to the one without, which can later be implemented as val.

See Programming in Scala:

Such parameterless methods are quite common in Scala. By contrast, methods defined with empty parentheses, such as def height(): Int, are called empty-paren methods. The recommended convention is to use a parameterless method whenever there are no parameters and the method accesses mutable state only by reading fields of the containing object (in particular, it does not change mutable state).

This convention supports the uniform access principle [...]

To summarize, it is encouraged style in Scala to define methods that take no parameters and have no side effects as parameterless methods, i.e., leaving off the empty parentheses. On the other hand, you should never define a method that has side-effects without parentheses, because then invocations of that method would look like a field selection.

Terminology

There are some confusing terminology around 0-arity methods, so I'll create a table here:

I sounds cool to say "nullary method", but often people say it wrong and the readers will also be confused, so I suggest sticking with parameterless vs empty-paren methods, unless you're on a pull request where people are already using the jargons.

() is no longer optional in Scala 2.13 or 3.0

In The great () insert, Martin Odersky made change to Scala 3 to require () to call a method defined with (). This is documented in Scala 3 Migration Guide as:

Auto-application is the syntax of calling a nullary method without passing an empty argument list.

Note: Migration document gets the term wrong. It should read as:

Auto-application is the syntax of calling a empty-paren (or "nilary") method without passing an empty argument list.

Scala 2.13, followed Scala 3.x and deprecated the auto application of empty-paren methods in Eta-expand 0-arity method if expected type is Function0. A notable exception to this rule is Java-defined methods. We can continue to call Java methods such as toString without ().

To answer your second question, just add an _:

scala> def foo = println("foo!")
foo: Unit

scala> def test(arg: () => Unit) = { arg }
test: (arg: () => Unit)() => Unit

scala> test(foo _)
res10: () => Unit = <function0>

scala> test(foo _)()
foo!

scala>