Hi quim!
paperclip is right and his links are good. That light has a "dual" nature has been known for a long time, but it was not until the end of the 19th century that physicists began to suspect that their particle and wave "disagreement" in fact was just two sides of the same coin.
In 1905, Einstein showed that light can behave as a particle with energy, known as the photon. However, the way light travels is wave-like in nature, thus there exists a phenomenon which has been named the "wave-particle duality".
You can read more about it
here.
Paperclip mentions the ether theory. How scientists came to understand that the ether did not exist is indeed an interesting piece of science history. You can read a brief notice on what it is and how it came into existence
here. I think the note is not compete - the belief that space was not empty existed long before Faraday and Maxwell. Newton had an ether theory which was important for his work on optics. It was
Isaac Newton who discovered that when light passes through a lens the light is broken down into its constituent colors (thus proving that white light is a mixture of many wavelengths).
Even today, there are still scientists who believe there is a form of ether permeating the Universe, but modern physics does not need it. The empty vacuum of space is not really empty, it contains enourmous amounts of potential energy and virtual particles pop in and out of existence all the time, borrowin energy from the vacuum. Here is an interesting slide show which describes it:
Physics of Vacuum Energy: Gravitation of the Casimir Effect.
I also found this interesting page about early theories of light and how it moves -
EARLY IDEAS OF LIGHT.
Tormod