The automated manual transmission is perhaps better known and more accurately described as the dual-clutch automatic, and it is an increasingly popular option. Though the dual-clutch automatic transmission became popular on high-end performance cars, such as Porsches and Audis, it is increasingly available on more mainstream models.
The dual-clutch automatic operates via two clutches, which are controlled by the car's computer network and require no input from the driver. As we discussed, when the clutch in a manual transmission is engaged, it disconnects the engine from the transmission to enable the shift. The dual-clutch automatic operates two different gears at once, which completes the shift while bypassing the power-disconnect stage. That allows a dual-clutch transmission to complete shifts much more quickly, since there isn't a "pause" while the engine and transmission try to match back up.
The car is faster since there is no interruption in power, the ride is smoother since it's all but impossible to pinpoint the moment of the gear change, and fuel economy is better because there is no power lost to inefficient shifts. You can read about dual-clutch transmissions in more detail here.
It's worth noting that some cars with dual-clutch automatics offer a manual shifting mode, usually via steering wheel-mounted paddle shifters, but the experience is not the same. Some performance enthusiasts may bemoan the loss of the "row-it-yourself" experience, since manually shifting is an enjoyable skill to practice and perfect, but if speed is the ultimate goal, it's hard to argue with the results of an automated manual transmission.