Postulated in 1971, a fourth passive circuit element called a memristor has been invented by a team from HP Labs. Circuit theory books, which will have to be rewritten, teach the existence and use of three passive circuit elements: the resistor, capacitor, and inductor. The memristor, short for memory resistor, changes its resistance based on the history of the flow of charge through the device. It essentially behaves like a non-linear resistor with memory. The device improves in performance the smaller it is made. The memristor can be used as both a digital and an analog device, depending on how current is passed through it. The applications are astounding, including computers that do not need to boot up, the elimination of disk drives, more energy efficient devices, and analog computers that can remember and associate patterns in the same way as the human brain.
Links: HP Press Release, HP Labs, Nature, EE Times, 1971 Paper in IEEE Transactions on Circuits Theory theorizing the existence of a memristor.