History
The history of audio recording is vast and full of invention, so I will cover a few key inventions.
The first invention of the microphone was concieved by Emile Berliner in 1876. The Bell Telephone Company quickly bought up his invention for $50,000 and began creating telephones in mass. It was from this invention that recorded audio was birthed.
Carbon Microphones
In 1878 an inventor by the name of David Edward Hughes came up with the first invention of the carbon microphone. Though the invention was not actually developed until the 1920s, it is still the basis for carbon microphone designs used today
Carbon microphones are still used today, though the use is rare. One example microphone is the Shure 104c. The main advantage of carbon microphones is that they do not require a large DC voltage signal to produce high level audio signals. This comes in handy for safety reasons, as sometimes it is not possible to have high voltages such as in mines. Also, they provide a good backup telephone system in case of emergencies.
Ribbon Microphones
In the 1920s the ribbon microphone was invented, once again changing the audio industry in a major way. These new microphones were able to record audio signals with unprecedented accurracy by using a very thin aluminum strip (or ribbon) as the diaphram/voice coil.
The biggest problem with this type of microphone is that the aluminum ribbons tend to be very fragile and may require replacement with even the smallest of spills. Today, however, designs have improved and it is fairly easy to get this ribbon replaced for most types of ribbon mics.
Ribbon mics are used very often today and in fact one of the highest demanded microphone styles available. The reason for this is their tendency to soften the more "harsh" frequency ranges, which typically range from 3kHz to 6kHz. In addition to this they have a rolloff of highs starting at about 10kHz. This makes them ideal for instruments that have a pronounced response in that range, such as string instruments and electric guitars.
Electret Capsules
Perhaps the most revolutionary design came in 1964, when James West and Gerhard Sessler patented thier design for the electroacoustic transducer. Most microphones that are commonly used today are either dynamic or condensor microphones, both of which are based on this technology. Dynamic microphones are cheap, durable, and effective while condensor mics are large, expensive, and for the most part capture audio with incredible sonic accuracy.
There is not one professional studio that does not have some sort of dynamic and condensor microphone. They are essential in recording.
These are some key inventions in the microphone industry, however there are far more inventions in audio as a whole. I have included some links with more information on the audio recording history in the relevant links tab to the left.