The first three types of electronics, resistors, capacitors, and inductors, were discovered very early, before 1900. It occured to people that logically there should be a forth type, but no one went very far with that idea. A mathematician, Leon Chua, proved mathematically that this forth type would exist and what properties it would have, but didn't build one. (He designed many other circuits, including some that are non-deterministic, an unusual trait for electronics.) This was in 1971.
An actual memristor wasn't built until 2008. 37 years later. It's still in the experimental stage, physically, but it implies some interesting things.
Especially in computers. Memristors could produce, according to electronics experts, a device that is a CPU, RAM, and a hard drive, all in one device. (It's a CPU because it can process information, RAM because it can store it [and reads and writes very quickly], and a hard drive because the information is not lost when the power cuts out.) It would enjoy capacities of terrabytes per cubic centimeter, and could be stacked together. This would be an impressively powerful computer that could be made literally arbitrarily large.
The future's so bright that I'll need to wear sunglasses.