My app store in Windows 8 has not the Windows 8.1 update.

• If you do not have automatic Updates on your computer you get this problem.

Do this:
Control panel > Windows update > Search for updates
When search is done do this:

1. Click "Important updates". (See Image)
2. Click the "Box" near "Names" so all becomes unchecked.
3. Check all the KBxxxxx80 to KBxxxxx89. (See Image)
4. Click "Install".
5. After install you should see the "Windows 8.1 Update" in your store app. (If not reboot and start over. You will get more KBxxxxx80-89 updates after you reboot.)