How to download the latest emails on IMAP?

Is it possible to download emails from a certain date? Never see this in the imap_ functions*

Is it possible to get the number of messages within mailboxes and to compare them. But if the letter is moved to another folder, it is highly likely that you will get out of sync client with the server.

As a variant I see only to take one look and replicated it already or not, if Yes then terminate. But it is also so-so option. I would like when taking trim already downloaded.

How is it done?