Desktop icons disappeared

Have you elected to keep Documents & Desktop in iCloud?

Open a Finder window and click on iCloud Drive in the Sidebar.

Shut down the computer. Wait 30 seconds. Restart into Safe Mode. If the icons have returned, then restart normally. Safe Mode is a pretty slow startup as will be the first restart after safe mode. This is normal.

While in safe mode you may want to do the following:

Repair the Drive for El Capitan or Later

1. Restart the computer and after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the side list. 
4. Click on the First Aid tab in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.