Over the past few years there has been a lot of fascinating work in molecular electronics. Because of the success of digital logic implemented in VLSI over the past several decades, molecular electronics researchers have focused most of their attention on implementing digital circuits using logic gates.
Early work included the identification of a molecular rectifier or diode, a device that allows electrical current to pass one way but not the other. Arranging diodes in a crossbar arrangement is a major step toward the implementation of complex logic circuits. Additional pieces required to make it practical include nanoscale wires, inverters, and amplifiers, and maybe a flip-flop.
Carbon nanotubes can have different chiralities, which give different electrical properties. Some chiralities give conduction so that the nanotube functions as a wire. Other chiralities give semiconductor behavior, introducing the possibility that a nanotube may be useful as a carbon transistor.
There was some very interesting work done by HP and UCLA in January 2002, basically a way to build a rectangular array of north-south and east-west wires, and connect them by fuses that could be selectively blown. That permits a lot of flexibility in wiring up circuits, which you need to do anything interesting. I haven't heard much more about the HP-UCLA work since 2002, though, and I wonder if they've hit some kind of stumbling block. Their work was based on rotaxanes and catenanes.
There is more to say on this topic, and it will merit another posting one of these days.