Network Thermostat

I wonder how the Web communicates with a remote programmable thermostat or other device?
I do not think the device must be connected to a telephone line or Wi-Fi!
Is it by radio signals or RFID, and if so, how does THAT?
Is the company selling the device must establish a global radio network?

Those I have seen a computer in the basement attached to your furnace, and the only son for the communication to the screen / keyboard (emperature sensor), which is just that, or for wireless keyboard or sensors.

The computers in the basement connects to your home network as well as any other computer in your home does, Ethernet or Wi-Fi