The fourth circuit element called “memristor”  is an intriguing case for the sociology of science  and it still unfolds. Especially annoying and I think entirely unnecessary are the detractors who do not grasp the trivial core issue. There are certain engineers that peddle mere technicalities as huge discoveries on the vixra crackpot archive after having been kicked out of the real (mostly non-crackpot) archive, claiming that the “memristor” is incomplete. So what? Being incomplete does not make it bad science, on the contrary. They hand easily refuted charges on a silver platter to Goliath so he can point to them laughing: “Look, all that criticism is mere confused schoolboys not getting it”.
There may also be serious plagiarism involved, but let us focus on the core issue, which is independent of technicalities about ‘pinched loops’ or that the actual devices have been around already since 1967 , before the real memristor was even predicted  in 1971!
That the 2008 claimed discovery is false can be easily understood , in fact, it is trivial: The prediction of the fourth basic circuit element called “memristor”, irrespective of engineering details, is based on electro-magnetic symmetry. Without magnetism, there are 2 basic circuit elements, namely resistor (R) and capacitor (C). However, because there is magnetism, they may have magnetic 'counterparts' (in a well defined sense), called inductor (L) and memristor (M). The inductor, for example a simple copper coil, of course exists. The memristor, just like magnetic charges (monopoles), probably does not , although the symmetry between electricity and magnetism allows and suggests them all. You do not need to know any more details in order to fully understand that 2 times 2 equals 4, not 3 or 5.
2 * 2 = 4
The 2 sides of the coin, namely electricity being one and magnetism being the second, that is what gives the second factor of 2, resulting in 2 * 2 = 4. In case there is only electricity (no magnetism), we have 2 * 1 = 2: No memristor and no inductor either. As you see, this is not even about the memristor. It is about something everybody knows: Without magnetism, there is no inductor! The name inductor means precisely that: It induces magnetic fields.
The devices described in  work perfectly well without any magnetism; the “discoverers” freely admit this with pride. There are ions that change the resistance of a thin film, much like you could attach a counter that looks at how much charge flows and adjusts the resistance accordingly via a knob (potentiometer). If we would accept such silly contraptions as the memristor (i.e. the fourth basic circuit element), then there would be 3 basic circuit elements in a world without magnetism*. Impossible!
These devices, properly called memristic devices, would work just as well without magnetism.
It comes even worse: The very argument  that was used to predict the memristor as a fourth basic element (M) from our well known 3 elements (R, C, L), that very argument could now be used in a world without any magnetism in order to demand a fourth element, again from the existence of 3, if there were such a thing as a memristor in such a world that could be added as a third element to the resistor and the capacitor (M, R, C). That fourth element would be the inductor (L) of course! An inductor, meaning something that induces magnetic fields, in a world without any magnetism!
It is ridiculous, yet because high profile people and a lot of money are involved, people defend the fake “discoverers” with desperate means. There is for example this archive paper (warning – a lot of pseudoscience finds its way onto the archive) that claims that because there is magnetic flux due to the oxygen vacancies, thus the devices are memristors. It is equivalent to arguing that because there is a fridge magnet glued under the counter that adjusts a knob on an adjustable resistor, therefore magnetism is involved and so such a contraption can count as a memristor. But fun aside - let us again get to the core issue:
Dear HP - where is the nano inductor without magnetic fields please? And another one: Why, if all of a sudden there are inductors that have no magnetic fields, why do we need to stop at 4? If the symmetry is not necessary, why you still sell the fourth element as the last one, as the big discovery that completes circuit theory? Why not have a fifth one, maybe seven?
Once more to all those who for example emailed me with such ideas as ‘non-magnetic inductors’ being coils made from non-magnetic material (righty - as if there is still magnetic material without magnetism - face palm): We are talking about a symmetry here. Symmetry, as clear cut as energy conservation due to time-translation symmetry (no, there is no perpetual motion machine, even if you use magnets). Fundamental symmetries are physics, they are not argued against with some engineering mindset drawing on strange old references about materials chemistry. The memristor was based on symmetry and it is therefore not just a memristic device.
Here once more a picture illustrating the underlying symmetry that suggests the true memristor, which has never been found and may well be impossible:
Illustrations  of the symmetry that led to proposing the memristor: (a) the tetrahedron spanned by the four fundamental circuit variables (current I, voltage U, electrical charge Q, and flux phi), (b) the relations and circuit symbols of the four basic two-terminal circuit elements that correspond to the four uncolored (thin) edges in (a).
* The strength of magnetism depends on the velocity of light c, so if c were much larger, there would be no magnetism measurable; we would have never discovered it even though we could still discover the thin film devices falsely called “memristor”.
 D. B. Strukov et al.: “The missing memristor found.” Nature 453, 80-83 (2008)
 S. Vongehr: “The Missing Memristor: Novel Nanotechnology or rather new Case Study for the Philosophy and Sociology of Science?” http://arxiv.org/abs/1205.6129
 F. Argall: “Switching Phenomena in Titanium Oxide Thin Films” Solid-State Electronics Pergamon Press 11,535-541 (1968)
 L.O. Chua: “Memristor – the missing circuit element.” IEEE Trans. On Circuit Theory CT-18, 507-519 (1971)
 S. Vongehr “Missing the Memristor.” Adv Sci Lett 17, 285-290(2012)