I wanted to be able to press a key in mutt which would run offlineimap in the background to get new messages, then ask Mutt to put them on screen. This line goes in my .muttrc:
macro index,pager @ "<enter-command>unset wait_key<enter><shell-escape>offlineimap -o -u quiet &<enter><sync-mailbox>" "Run offlineimap"
It defines a macro which can be run in the index or the pager of mutt by pressing the @ key.
First it stops mutt from asking the user to press any key to continue once the shell command is finished.
Next it invokes offlineimap in the background (&). Then afterwards it syncs mutt with its mailboxes (:sync-mailbox).