A report from physorg.com points me at a paper in PNAS, where HP researchers say they've mixed up memristors and transistors on the same silicon substrate "to form fully integrated hybrid memory resistor (memristor)/transistor circuits. The digitally configured memristor crossbars were used to perform logic functions, to serve as a routing fabric for interconnecting the FETs and as the target for storing information." (As PNAS - the Proceedings of the National Academy of Sciences - publishes open access papers, you can see for yourself.)
This is intensely interesting, both for the speed at which the technology is being integrated into standard electronic production processes and for the direct application of these experiments to real-life uses. Memristors are resistors that change their resistance depending on the voltage across them - and, crucially, retain that changed state when the voltage is removed. As this state can be one of lots of conditions, a single memristor can theoretically hold quite a few bits of data; in these experiments, however, they were just used as on/off devices.
But it all worked, with a 21x21 crossbar of memristors happily programmed and used in a number of modes. The top speed of one of the device configurations was a very leisurely 2.8 kHz - only a million times slower than a modern processor - although it could be persuaded up to the heady slopes of 10kHz. The researchers put this slow speed down to the measuring cabling, although I don't quite understand that. Even I've got oscilloscope probes orders of magnitude better than that - and it's not that hard to build a buffer amp.
Another big thing the paper reports is self-programming, where a circuit containing memristors is able to learn from its own outputs. That opens the way for simulations of synapses, as well as various interesting logic designs, that don't need the complexity of explicitly saving or restoring state.
So progress is rapid, and progress is good. I would take exception to one reported quote from the physorg.com piece, though:
"It actually takes at least a dozen transistors to mimic the electrical properties of a single memristor,” Stan Williams of HP told PhysOrg.com. “Thus, for circuits that require some type of latching or other function performed by a memristor, it is at least conceivable for a designer to replace several active transistors with one passive memristor, which is much smaller than a single transistor. This maintains the capability of the chip while decreasing the number of transistors, which saves both silicon area and power. Thus, it may be possible to continue the equivalent of Moore's law for a couple of generations not by making transistors smaller, but by replacing some subset of them with memristors."
This seems dodgy logic (of the human kind, not the electronic). It may be true that you need lots of transistors to simulate a single memristor - in fact, I'm sure it is - but that doesn't mean you can replace any particular combination of transistors with a memristor - only a collection that happens to look like a memristor in the first place. It takes yeast and grain to make beer and bread, after all, but you can't replace bread with beer. (I have tried.)
But that's a bit churlish. We won't really know what we can do with memristors until they get out there into the real world and lots of engineers start playing around in lots of ways with them. So far, though, it's looking good.