These are all paintings, but, as I’ve said, you may use almost any kind of media to express yourself. Remember, you are trying to capture the essence of a person, not his likeness (though you may do that, as well).
Marsden Hartley painted his dashing (and recently deceased) friend like this:
This is the poet William Carlos Williams. The portrait includes one of his poems.
Picasso painted his girlfriend like this. True love?
Know anyone like this?
This is Arcimboldo’s patron (and Holy Roman Emperor). Why would he paint him like this?
This is a portrait I did of someone I used to know. She floated through life.
Here is a portrait I did of someone who has tried to please others for so long that he has lost his sense of self.