In 1864 James Clerk Maxwell showed mathematically that electromagnetic waves could propagate through free space. This led to a series of experiments in Early Radio Transmission leading up to the First Live Radio Recital in 1920 - wikipedia 
The effects of electromagnetic waves (then-unexplained "action at a distance" sparking behavior) were actually observed before and after Maxwell's work by many inventors and experimenters including: - George Adams (optician, younger) (1780-1784) - Luigi Galvani (1791) - Peter Samuel Munk (1835) - Joseph Henry (1842) - Samuel Alfred Varley (1852) - Edwin Houston - Elihu Thomson - Thomas Edison (1875) - David Edward Hughes (1878)
Edison gave the effect the name "etheric force" and Hughes detected a spark impulse up to 500 yards (460 m) with a portable receiver, but none could identify what caused the phenomenon and it was usually written off as electromagnetic induction.
In 1886 Heinrich Rudolf Hertz noticed the same sparking phenomenon and, in published experiments (1887-1888), was able to demonstrate the existence of electromagnetic waves in an experiment confirming Maxwell's theory of electromagnetism.
The discovery of these "Hertzian waves" (radio waves) prompted many experiments by physicists. An August 1894 lecture by the British physicist Oliver Lodge, where he transmitted and received "Hertzian waves" at distances up to 50 meters, was followed up a year later with experiments by Indian physicist Jagadish Bose (Jagadish Chandra Bose) in radio microwave optics and construction of a radio based lightning detector by Russian physicist Alexander Stepanovich Popov.
# Wireless Telegraphy
Starting in late 1894, Guglielmo Marconi began pursuing the idea of building a wireless telegraphy system based on Hertzian waves (radio). Marconi gained a patent on the system in 1896 and developed it into a commercial communication system over the next few years.U.S. Supreme Court
In addition to Marconi, two of his contemporaries, Nikola Tesla and Nathan Stufflefield, took out patents for wireless radio transmitters. Nikola Tesla is now credited with being the first person to patent radio technology. The Supreme Court overturned Marconi's patent in 1943 in favour of Tesla - thoughtco.com
Early 20th century radio systems transmitted messages by continuous wave code only. Early attempts at developing a system of amplitude modulation for voice and music were demonstrated in 1900 and 1906, but had little success. World War I accelerated the development of radio for military communications, and in this era the first vacuum tubes were applied to radio transmitters and receivers.
# Radio and Television
Electronic amplification was a key development in changing radio from an experimental practice by experts into a home appliance. After the war, commercial radio broadcasting began in the 1920s and became an important mass medium (mass media) for entertainment and news. World War II again accelerated development of radio for the wartime purposes of aircraft and land communication, radio navigation and radar.
After the war, the experiments in television that had been interrupted were resumed, and it also became an important home entertainment medium.