Theoretically, Continuous Variable Transmission should offer optimised fuel economy as well as acceleration. 

All previous CVTs, from thew likes of DAF, Nissan, Subaru, Honda, Fiat or Ford, barely offered a smooth transmission. never mind the theorectical gains. They might be cheap alternatives to automatic, but have been unable to match manual gearboxes in the real world. 

Now  Audi is claiming a real improvement based on the A6:
  

 

0-60 mph

Fuel consumption
A6 with 5-speed manual

8.2 sec

9.9 litre / 100km
A6 with 5-speed Tiptronic

9.4 sec

10.6 litre / 100km
A6 with Multitronic CVT

8.1 sec

9.7 litre / 100km

 

The Multitronic differs from conventional CVT by two things :
1) it uses chain instead of belt as the media to transmit torque and vary gear ratio.
2) it has a torque sensor.

Most previous CVTs use a steel V-section belt developed by Dutch CVT specialist Van Doorne. How much torque the CVT can  withstand depends on the design of belt, which at its best (Nissan Primera) is 150 lbft. of torque.   Instead, Audi developed a chain to replace the belt. The steel chain consists of 1025 link plates and 75 pairs of pins. It is almost as flexible as a V-section belt but much stronger. It can handle up to 221 lbft of torque.

Another breakthrough is the use of torque sensor. It ensures the pulleys clamp the chain with sufficient contact pressure, but not excessivly. Conventional CVTs always apply exces  pressure in order to cover all the possible conditions of use. Excessive pressure results in worsend fuel efficiency and wear. Fuel economy is further enhanced by the extra-wide gear ratio range - 6.05 : 1, compared with the  5 : 1 of a conventional manual gearbox.

The program is also smart in that. Firstly, it monitors engine speed to eliminate the "rubber band effect" which exists in previous CVT designs. It ensures that the engine revs increase with increasing driving speed. Secondly, from the pedal action, it recognizes whether the driver would prefer to drive in a more performance-oriented or consumption-oriented manner,and   chooses the right ratio.

Lastly, it provides 6 sequential "manual" ratios for those who like more involvement. It enables engine braking as desired. Like Tiptronic S, there is also an optional steering wheel control for upshift and downshift.

Most modern CVTs use electro-hydraulic clutch or torque converter, but the design Audi uses a multi-plate clutch, which is more complicated but enables a smooth yet responsive transition.