The fourth circuit element called “memristance” is an intriguing case for the sociology of science  and it still unfolds. Especially annoying are pseudo-critics who do not grasp the core issue. Certain engineers peddle mere technicalities, claiming that the “memristor” is incomplete. So what? Being incomplete does not make it bad science. They hand easily refuted charges to Goliath so he can point to them laughing: “Look, all that criticism is mere envious pseudo-science”.
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 devices have been around since 1967 , before the real memristor was even predicted  in 1971!
That the 2008 claimed discovery is false can be easily understood : The prediction of the fourth device is based on electro-magnetic symmetry. Without magnetism, there are 2, 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, a simple copper coil, of course exists. The memristor, just like magnetic charges (monopoles), probably not .
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 without any magnetism. 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. If we would accept such silly contraptions as the memristor, then there would be 3 basic circuit elements in a world without magnetism. Impossible!
Memristic devices, would work just as well without magnetism.
The very argument  used to predict the memristor as a fourth device from our well known 3 (R, C, L), that very argument could now be used in a world without any magnetism to demand a fourth device, 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 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, 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 the contraption is a memristor.
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.
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 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)