This article from Ars Technica talks a little bit about memristors and HP's plans for "The Machine". The original plan was for The Machine to demonstrate this technology, but HP ended up removing feature after feature (including memristor technology) before it's release. They quote John Sontag from HP in the article:

"The simplest way to think about it is this—take a DRAM DIMM out, and put a memristor DIMM in,” said Sontag. “You now have another pool of memory that’s denser and nonvolatile. It’s a new class of memory—the consequence for operating systems is that moving stuff around from I/O devices [to and from disk] becomes unnecessary."

https://arstechnica.com/information-technology/2014/06/hp-la...