Or do you just export from crm and import new list into a new mail chimp list each time?
Yes, unfortunately it has to be done each time. At the moment, that's monthly for us.
It would be a home run if AwareIM allowed the integration with MailChimp API so a BO could be kept totally in sync with a Mail Chimp list.
And if so how do you get the unsubscribes back from mail chimp into your crm (or don't you bother)?
In our case, unsubscribes from MailChimp don't matter to our CRM. But they could be exported from MailChimp and imported into AwareIM CRM if you'd like.