"Following up on" something means reviewing it again later. You "follow up" to:

• make sure that something gets done:
  

  They're not very reliable. You have to follow up with them two or three times to make sure that anything gets done.

• ask more questions about something that you didn't understand:
  

  Make sure to follow up with the professor after class or during office hours if there's anything you didn't understand.

• get an answer to a question that someone didn't answer before:
  

  I just wanted to follow up and see if you've given any thought to my offer.

"Follow up" can be used by itself:

You should definitely follow up.

If you want to mention the topic, use "on ___":

Can you follow up on the pricing estimates?