Problem with Messages which has stopped syncing between Macbook pro and iPhone How do I re-sync my iPhone Messages with my MacBook pro Messages?
More information would help answer this question. For example, Are you finding that messages on one platform are not updating at all? For example, the iPhone? If so, I would suggest trying steps such as these:

1) Settings --> Messages --> iMessage (cycle it off and then back on)
2) Log out and back in with your AppleID
3) Turn the phone off and back on.

If the problem is on the MBP, then I would similarly start with Messages-->Preferences and then sign out and back into the iMessage service.

If those steps don't help, please characterize the symptoms in more detail.