How does the mobile phone work?

Mobile phones are radio phones that route their calls to a network of masts linked to the main public telephone network.
Mobile phones use electromagnetic waves
These are waves that allow you to send and receive the information (sounds) that normally travel through wires.
Whether you are sitting at home, walking down the street, driving a car or travelling on a train, you are always surrounded by a sea of electromagnetic waves.
TV and radio programmes, car radio signals, cordless phone calls and even wireless doorbells - all of these things are using electromagnetic energy: undulating patterns of electricity and magnetism that zigzag invisibly through space, at the speed of light (300,000 km or 186,000 miles per second).
When you talk into your mobile phone, a tiny microphone inside it converts the high and low sounds of your voice into a corresponding pattern of high and low electrical signals. A microchip inside the phone converts these signals into strings of numbers. The numbers are packaged into a radio wave and broadcast from the phone's antenna.
The radio waves travel through the air at the speed of light until they reach the nearest mobile phone mast.
The mast receives the signals and passes them on to the base station, which efficiently coordinates what happens within each part of the cellular network, known as a cell.
From this base station calls are broadcast to their destination.
Calls made from one cell to another cell travel on the same network to their destination, as they are routed from the base station closest to the recipient phone. Calls made to a mobile phone via a different network or landline follow a longer path. They have to be routed to the main telephone network before they can reach their ultimate destination.
Land lines carry calls along electrical wires. Landlines are not unlike the toy phones you can make from a piece of string and a couple of cans of baked beans.
The words you speak travel over a direct, wired connection between two phones.
How is it different from a mobile phone to be able to send and receive calls without wired connections of any kind? How does it happen?
Mobile phones are by far the fastest-growing source of electromagnetic energy in the world around us.