come up

1.  Arise, present itself, as in This question never came up. [Mid-1800s]
2.  Rise (from a lower place to a higher one) as in We'll leave as soon as the sun comes up. [9th century]
3.  Also, come up to. Approach, come near, as in He came up and said hello, or The dog came right up to Nora. [Early 1700s]
4.  Also, come up to. Rise in status or value, be equal to, as in His paintings will never come up to his teacher's, or This officer came up through the ranks. [c. 1600] A variant is come up or rise in the world, used for someone who has risen in rank, wealth, or status; for example, He has really come up in the world--he now owns a yacht, or I could see at once that she was a woman who would rise in the world. Also see the subsequent idioms beginning with come up.

The verb has 12 meanings:

Meaning #1: bring forth, usually something desirable

Meaning #2: occur
  Synonym: arise

Meaning #3: move toward, travel toward something or somebody or approach something or somebody
  Synonym: come

Meaning #4: come to the surface
  Synonyms: surface, rise up, rise

Meaning #5: originate or come into being
  Synonyms: arise, bob up

Meaning #6: move upward
  Synonyms: rise, lift, arise, move up, go up, uprise

Meaning #7: be mentioned

Meaning #8: start running, functioning, or operating, as of lights or power
  Synonyms: go on, come on

Meaning #9: get something or somebody for a specific purpose
  Synonyms: line up, get hold, find

Meaning #10: come up, of celestial bodies
  Synonyms: rise, uprise, ascend

Meaning #11: gather together over time; as of money or other resources
  Synonyms: scrape, scrape up

Meaning #12: gather or bring together
  Synonyms: muster, rally, summon, muster up