why won't imessage sync between iphone and imac?

iMessage simply won't sync between my iPhone and my computers. I have tried advice that I found online:

make sure that conversations all start from one e-mail address;

make sure the phone number is associated with the account;

turn iMessage off on phone and computer, wait a few seconds and then turn on again.

But it is still as if I have two messaging services: one on my computers and one on my phone. To add to the confusion, the iMessage windows on the computers are different as well!