Devices, systems, and methods of wirelessly controlling appliances and electronic devices, such as ceiling fans, air conditioners, garage doors, or the like. A receive-only garage door system is wirelessly controlled by a proprietary remote control unit. A cloning unit is able to clone or duplicate the proprietary wireless signal, and to replay it or re-generate it in response to a triggering command that a user submitted via a smartphone or tablet; thereby enabling to control such garage door system via mobile electronic devices. The cloning unit utilizes recording of the wireless signal payload and carrier frequency; wireless signal analysis; image analysis of the appliance or of the remote control unit; queries to a remote server to obtain properties of the proprietary wireless signal; or other techniques of signal analysis or duplication.