Memristors were originally proposed as a thought experiment, describing a theoretical fundamental circuit component, like a resistor or capacitor. The basic idea is that their resistance depends not on the current flowing through them now, but on the integral of the current with respect to time. This means that their resistance changes depending on previous current flow, and means that they can be used to store a value by passing some current through them and then measuring their resistance.
Until 2008, memristors were entirely theoretical. In 2008, HP researchers produced the first working prototype. Unlike the other technologies we've looked at, memristors are not likely to be shipping in consumer hardware any time soon. Current prototypes are very fastaround 1ns access timesbut they are still a very long way away from the kind of storage density that Flash has.
The memristor is much more interesting as a theoretical development. Like the transistor, it can be used to create solid state storage, but it's also potentially useful for computation, too.