Throwing any conventional method of fire extinguishing out of the window, DARPA has been exploring the use of electricity and sound to put out the flames.
This began with changing the initial understanding of fire, from a chemical stance to a physics point-of-view, which labels it as a cold plasma: a low energy, ionized gas. With this in mind, DARPA has been able to create two entirely new firefighting methods. The first using an oscillating array of electrons, titled "ionic wind," which effectively blows out the fire using the aforementioned electrons. And the second being to create an acoustic field which disperses the flame via increasing the air velocity, causing the temperature to drop.
While these have been proven to work in lab tests, this is still far from being used in the real world. Makes for an awesome discovery though.