Memristor do no computation at all. It follows the same idea as the described RRAM. High density, low cost, persistent, low power consumption, high write/read throughput, low latency. To the exception that it could even replace RAM, not only nand devices. I don't remember of the top of my head reading performance but it was clearly closer to RAM levels.

A memristor can do computation, but you don't have to do computation.

Like like a regular transistor can be used for computation or ram.

A memristor can be set up as a logic element that does computation, or as a memory storage element, just like a transistor (only persistent).

For some strange reason, the tech press took this to mean that a memristor array can be dynamically reconfigured to act as logic or ram in the same device. This is mostly false -- while yes, this kind of devices can be built (with transistors, they are typically called field-programmable gate arrays, or FPGAs), this requires you to be able to reconfigure not just the gates, but all the wiring that goes into them, meaning that a reconfigurable array has to be more than an order of magnitude larger, and a few times slower than a non-reconfigurable one.

You never want to use an FPGA for ram because you can get proper, non-reconfigurable ram for (way) less than tenth of the cost. You never want to use a fpga for logic if you can afford an asic, because you can be several times faster with hard-baked logic.

Memristors will mean nice FPGAs that retain state on power down, but they will not mean a revolution of dynamically reconfiguring devices.

Oh, and memristor logic is slower than transistor logic (you can do with less gates, but the gates switch slower) so the ability to use memristors for logic elements will initially mostly be a win in memory devices where the necessary logic to manage the device can be made out of the same structures the device is made of.