IBM is doing some great work in advancing carbon transistor technology.

IBM Researchers today announced that they have demonstrated the operation of graphene field-effect transistors at GHz frequencies, claiming the highest frequencies reported so far using the non-silicon electronic material.
IBM is a long-time proponent of graphene — a special form of graphite, consisting of a single layer of carbon atoms packed in “honeycomb lattice” — as a material for building nanoelectonic circuits smaller than those in today’s silicon-based computer chips.
The company in March announced that it discovered a way to suppress unwanted interference of electrical signals that are created when shrinking graphene. That development was followed closely by research from the University of Maryland that found that electrons travel more than 100 times faster in graphene than in silicon.
Specifically, IBM said today that its scientists have fabricated nanoscale graphene field-effect transistors and demonstrated the operation of graphene transistors at the GHz frequency range, establishing scaling behavior for the first time.

Faster transistors are only part of the equation though. Today the wires in chips represent about one half the delay between circuits. So even if transistor delays went to zero chip speed would only double.
Still, this will help and it may lead to other discoveries that will change the way chips are made. For instance DNA might be designed that could grow chips out of carbon. But we are a ways off from that.
Here is what DARPA has to say about their graphene transistor program.

The Carbon Electronics for RF Applications (CERA) program will develop wafer-scale graphene synthesis approaches and ultra-high-speed, low-power graphene-channel field effect transistors for RF/mm-wave circuits. The many desirable material properties of the novel graphene films, including ultra-high mobility, high saturation velocity, high current carrying capability, excellent thermal conductivity, ultra-thin geometry and the potential to integrate with traditional CMOS processes, offer the potential for graphene-based transistors with high promise for high-performance, high-integration-density RF system-on-chip applications. For this reason, the CERA program focuses on developing innovative approaches that enable revolutionary advances in materials science, epitaxial growth, transistor development, and RF circuit design. Desirable properties of CERA transistors include high mobility, high cutoff frequencies (ft and fmax), high transconductance, low noise, and low voltage operation. In addition, graphene-channel devices also offer low parasitic resistances, excellent electrostatic scaling and high integration potential with silicon CMOS. The CERA program will culminate in a demonstration of high performance W-band (> 90 GHz) low noise amplifiers (NF < 1dB) making use of graphene transistors on wafers with diameters > 8 inches.

Low parasitic resistances could speed up the other half of the equation – the delay between transistors.
If the material can operate at higher temperatures than silicon it could also be the foundation of more compact high power electronics. High power MOSFETs are essentially hundreds of thousands of small transistors connected in parallel. If they can be made smaller, faster, and cheaper they could lower the cost of high power electronics such as those used in converting solar cell energy to AC line current or making hybrid, plug in hybrid, and battery powered auto electronics smaller, cheaper, and more efficient.
We do have quite a ways to go to turn lab experiments into a production process. However, there is a start here and a proof of concept so the rush will be on. We are quite a ways ahead of where we were in 1925 when Julius Edgar Lilienfeld invented the Field Effect Transistor, but no one knew how to reliably manufacture them. The kinks were not sufficiently ironed out in the manufacturing process until the early 60s although the bipolar junction transistor was made to work in the 50s.
Cross Posted at Power and Control