Memristors are not yet(2010) in commercial electronics. It is unclear how much influence this new component will have, and in which areas. Some believe that non-volatile memory for computers (hard drives and flash memory) is a possible site. Both the storage density and access times may be better than with current technology. An interesting area is the connection between artificial neurons, ie the artificial synapses.
In April 2010 according to HP and Stanley Williams in 2013 that they plan to go commercial with memristorer used something like flash memory used today. Also within the signal processing and control can be particularly useful memristors.
Chua describes himself now memristor tech he calls memcapacitors and meminductors, and is working on with his theories about the fundamental components in electronics. He believes that memcapacitors can be just as helpful as memristors, because they have no resistance.
One of the holy grails that HP is pursuing is fabrication of 3D chips using memristors.