I cant find a recent iphone backup.

Are you backing up to iTunes or iCloud?

If you're backing up to iCloud, it should back up daily when the phone is connected to power and wifi, and in standby.

If you're backing up to iTunes, it should back up every time you plug it in to sync.

And what are the circumstances?

If you're trying to restore a backup to a new or replacement device, you probably need to update the version of iOS it's running first.

You can not restore a backup made on a newer version of iOS to a device running an older version.

You can only find the ones you created.

No. It only "updates" the last complete iCloud backup.