Mnemonics

"pair", "twin", "ditto", "reflection", "aspect"
-- used to alias identifiers
-- used to create associative pair objects
-- used in package namespaces
-- everyone wants the colon

Used alone

: after a identifier at a statement boundary creates a label as in common parlance
: after an identifier is an invocant marker for indirect object syntax

Operators containing this character

:: sigil and nesting separator for packages (and consequently, types)
: before () creates a Signature object
:= aliases an identifier via runtime binding
::= aliases an identifier via compile time binding
.: dotted postfix form of prefix operator
.:: a class qualified method call
=:= container identity comparitor

When used inside regexes

Special Variables

:: may often be seen after sigils with other special symbols but is only for scoping. Look in this section on the other characters' pages.

As an adverb

: introduces an adverbial Pair constructor which includes also radix in literal numbers.
If you have a short-form adverb you don't understand, see this section in the page for the character after the colon.

Other Uses

: after a parameter name in a Signature "names the invocant"<>

Hyper operator and meta operator restrictions

Old, deprecated, or other language uses

? : the ternary operator from perl5 and other languages is ?? !! in perl6