Showing progress for long process?

I’ve got a plugin that allows mass-importing of posts based on files (it’s a webcomics thing). On an admin page, administrators can select an arbitrary number of files, hit Submit, and a post is generated for each one. The actual PHP that processes this is on the admin page itself.

This works great, but if there are a lot of files to import, it can take a long time. Obviously, this is not a good user experience, as WordPress displays nothing until it’s finished processing the entire thing.

Does anyone have a method (maybe involving AJAX?) that would allow an admin page to do this process in the background and provide status updates, maybe using a progress bar?

I note that some processes — such as upgrading WordPress — give status as it happens, such as “Unpacking the Update.” How does it get around the “do the whole thing, then display” feature of PHP in cases like this?