Memristors were conceived by electrical engineer Leon Chua in his seminal 1971 paper "Memristor--the Missing Circuit Element" (IEEE Transactions on Circuit Theory). His peer-reviewed claim startled electrical engineers by detailing how there was a "missing link" in circuit theory.
By mathematical necessity, according to Chua, a fourth passive electronics component--after resistors, capacitors and inductors--must exist. His argument was reminiscent of the inventor of the periodic table, Russian chemist Dmitri Mendeleev, who claimed that by mathematical necessity there were missing elements in the periodic table that must exist. Both were right. Mendeleev's missing elements were eventually discovered, and in 2006 Hewlett Packard Senior Fellow Stan Williams likewise discovered Chua's missing-memristor in a common semiconductor material.
Chua called his fourth passive circuit component a memristor, because it "remembered" the amount of current that had recently been flowing through it by changing its internal resistance--making it a memory-resistor. HP's formulation was titanium-dioxide, but since them many other semiconductor manufacturers have come forward to disclose that they had also been working on memristive materials in their efforts to build a universal memory type--called a resistive random access memory (ReRAM).
As a result, approximately 40 years after memristors were postulated by Chua, these materials are finally achieving widespread commercialization as universal memory chips that are nonvolatile, denser than flash, and yet faster than DRAM. A remarkable spectrum of semiconductor houses are promising memristive microchips, some as early as 2013, including Adesto Technologies, Elpida, Fujitsu, Global Foundries, Hewlett Packard, Hynix, IBM, Macronix, Nanya, NEC, Panasonic, Rambus, SanDisk, Samsung, Sharp, Sony, ST Microelectronics, Winbond, 4DS, and several research labs like IMEC collaborating with foundry partners like TSMC.
What you may not be aware of, however, is that the next 40 years are likely to be even more significant for memristors, as the basis of a new era of cognitive computers based on the architecture of the human brain. Spear-headed by the Defense Advanced Research Projects Agency (DARPA) program called Systems of Neuromorphic Adaptive Plastic Scalable Electronics (SyNAPSE) research labs are pioneering a new era of cognitive computers that are light years beyond artificial intelligence (AI). Participants included IBM, Hewlett Packard, and HRL Labs in cooperation with Boston University, Columbia University, Cornell University, Stanford University, University of California at Merced, and the University of Wisconsin at Madison.
Chua anticipated the application of memristors to artificial neural networks as far back as 1976 in his Proceedings of the IEEE paper Memristive Devices and Systems where he noted that the neuroscience standard model for neurons--the Hodgkin–Huxley model--was mathematically identical to a memristor.