wise guy noun

1. A conceited, over-confident person
2. A smart alec
3. A member of the Mafia (US inf)

wiseˈ-heartˈed adjective

1. Having wisdom
2. Prudent

wise man noun

1. A sage or elder
2. A wizard, magician or seer (dialect)

wise woman noun

1. A witch or seeress
2. A midwife (Scot)

be (or get) wise to (informal)

To be or become aware of

never, no, none (or not much or not any) the wiser

Still in ignorance

put someone wise (esp US informal)

To put someone in possession of essential information, make someone aware (with to)

the Wise Men (of the East), the Three Wise Men

The three Magi (in some traditions kings) who according to St Matthew's Gospel came to worship the baby Jesus at Bethlehem

the wiser for

Having learnt sense from (some salutary experience)

wise after the event

Only too aware of how something could have been avoided, done better, etc, when it has already occurred

wise up (slang)

To make or become aware, informed, etc