Some quick bits taken from the video (all are based on current findings; more than just theories, but not at fullscale production):
A. Storage of up to a petabit per centimeter.
B. Processing power equivalent to IBM's Big Blue on a 1cm chip.
C. Potentially infinite lifetime for storage (so, not like RAM, more like hard drives, except better)
D. Performance per watt by size is approximately 2 orders of magnitude better than today. This is much higher/faster than what would be realized following our current path down Moore's Law.
E. A memristor chip can be vast amounts of storage, act as switches, or do logic. Think RAM and CPU dynamically within the same chip, split among the memristors dynamically on the fly.
Note that they have already started making memristors, but simply need more engineering to reduce the scale, make it more efficient, and implementing it into computing technology (since it is not as simple as replacing a CPU, but requires a whole new way of thinking about computers).
I'm sure the idea of memristors isn't news to most of you, there's been talk for a couple years now or more about them. But this is by far the most detailed (and sometimes overly so) video I've seen about it. All the good bits about what is possible with said technology starts about halfway in, if you want to skip the design and logic behind it.