Phones have come a long way since the early days of invention, but still operate under the same basic principles! Phone transmit sound waves through wires, which may then pass from your home to a concentrator, which basically merges and digitalises your voice, along with many others nearby, and transmits them along fibre cables.
Mobile phones act differently, almost like two-way radios. They send electromagnetic microwaves from base station to base station. The waves are sent through antennas. This is called wireless communication.