My Windows 10 Messaging app seems to have problems. Until September 10th my SMS messages were showing up. Now they do not. I'm running 10.0.14393.447.
The settings page on the Messaging app also looks strange, it looks like:
Settings
About this app
Windows Messaging 3.19.1001.0
(c) 2016 Microsoft Corporation.
All rights reserved
That's pretty much it. There aren't really any settings there. I also have a Lumia 650 Windows 10 phone that's on anniversary update.
I can't see a way to repair or uninstall/reinstall the Messaging app.