I still don't have a way to save attachments. With an Office file (like Word) I get these four selections:

Preview: Shows it to me but I can't edit it.
Edit in Browser: I can edit it in whichever browser I'm using. When I go to the File tab to save it, I see this:

Save as: Saves a copy online. I don't know where it goes.
Download a copy: Might go to my Downloads folder, I can't tell.
(skipping PDF and ODT options)
At the bottom of the tab, to taunt me, is this:

Edit in Word Desktop App: Lets me know it's being uploaded to OneDrive. When it opens, I have the opportunity to save it... to OneDrive. Where do things saved to OneDrive go? As far as I can tell Outlook wishes it into the cornfield.
Save to OneDrive: I HAVE NO IDEA WHERE IT GOES.
With a non-office file I get this:

Preview: I see it in a black box. It cannot be opened or edited. (I get no option to open in Photoshop)
Save to OneDrive: WHERE DOES IT GO??? INTO THE CORNFIELD.
I'm using Outlook on my desktop.