To come towards, to approach.
I was standing on the corner when Nick came up and asked for a cigarette.
To emerge or become known, especially unexpectedly.
Unless anything comes up, I'll be there every day this week.
To come to attention, present itself; to arrive or appear.
At some point in the conversation my name came up, and I readily agreed to their proposition.
To appear (before a judge or court).
He came up before a judge and was fined a thousand dollars.
To draw near in time.
The summer holidays are coming up.
(of a heavenly body) To rise (above the horizon).
It'll be warmer once the sun comes up.
To begin to feel the effects of a recreational drug.
I could tell from her expression that she was coming up already.
(Oxford University) To arrive at the university. (Compare go down, send down.)