offlineimap

OfflineIMAP is software that downloads your email mailbox(es) as local Maildirs. OfflineIMAP will synchronize both sides via IMAP.

IMAP's main downside is that you have to trust your email provider to not lose your email. While certainly unlikely, it's not impossible. With OfflineIMAP, you can download your Mailboxes and make you own backups of your Maildir.

This allows reading your email offline without the need for your mail reader (MUA) to support IMAP operations. Need an attachment from a message without internet connection? No problem, the message is still there.