I have to archive some of my messages but can't find anywhere how to do that - my only alternative is to delete some..... I have searched the forum, no success, sorry.......
Click on Settings at the top right. Then under My Messages click Inbox. There's a little box to the right of where it tells you how many messages you have. Click that to select all. Then go to Sent Items and do the same.
Scroll down just past the last message and there's a drop down menu that tells you how many messages are selected. From there you can download as XML, CSV or TEXT.