Air compressors have been used throughout history however, air compressors that were in use thousands of years ago worked in a much more simplistic way than they do today. If you think about the basic action of an air compressor; free air enters a small chamber where pressure is built up, this is then released. An example of this is using bellows to increase combustion of a furnace. When the handles of the bellows are opened air enters the cavity. As the handles are opened, air is forced out at a higher pressure. Medical breathing apparatus used in hospitals work in much the same way.
During the industrial revolution the mechanical air compressor was created and began to be widely used. This led to the development of the air compressors that we know today. We now use air compressors that are much more technologically advanced. Piston compressors are generally used for car engines. For industrial machinery, rotary compressors are usually used as they produce large volumes of compressed air.