Radio waves (that's the stuff your antenna detects and is brought down to the receiver so you can hear it) was first mathematically proven to exist by James Clerk Maxwell. This was then proven in a lab by Heinrich Hertz. (yes this is the guy the unit Hertz as in Megahertz is named after) Radio waves are form of Electromagnetic radiation. Visible light is also a form of this kind of radiation
The next important invention was the spark-gap transmitter. This early device was used in wireless transmissions in the first "era" of radio. These transmissions were received on a device in many instances called a Coherer. This device was not designed for voice applications per se but was used mostly for morse code transmissions.
Next comes a man named Guglielmo Marconi. He is credited by many as the father/inventor of the radio. His work was mainly in the area of long distance transmissions. His experiments were the first to prove that for long wave and medium wave transmissions nighttime propagation was better.
Next I should mention mention two people that had a lot to do with the direction of radio over the time period ranging from about the 1880's up until about the 1930's. These two people were Nikola Tesla (my personal favorite) and Ernst Alexanderson. Both made inventions that were used in early radio and you should look them both up.
An early radio that is still in use today in some areas is a Crystal Radio. This was a radio that used a crystal and only the power in the radio wave itself to allow detection and listening to a radio signal. This crystal was an early type of diode (a device that only allows power to move in one direction). It was first used by one Jagadish Chandra Bose in 1894
The next major invention in the world of radio was the Vacuum tube (a lot of big old radios use these) They were used a lot by early inventors but it was in the early 1900's that an Englishman by the name of John Ambrose Fleming began using the rectifying ability of the diode tube to receive radio signals.
During the 20's through 40's a number of things were done including the following:
The next major step in radio was the advent of the inexpensive solid state diodes and the transistor. These two inventions allowed radios to get much smaller and easier to produce.
There are other inventions and updates that have been made over time but these, in my opinion, are the major milestones
that put radio on the map.
Check back later, I may add more to this as time allows