Turning on the Airplane Mode will disable all wireless communications.
Making calls, Bluetooth and Web access are restricted when this feature is turned on.

Thanks for the reply to my question. I think I have that function turned off, because all I get Is "No ID" no matter who the caller is. What is "Airplane Mode"?

If the number is saved on your contacts list, then the name assigned to that number will be displayed on your phone's Call History. If you don't have the number saved in your contacts list, then only the caller's number will appear, unless you're with Rogers or Fido and you added the Call Display with Name Display add-on to your plan.