Virtually unheard of just ten years ago, more and more cars these days are being offered with some form of paddle shifter. Not all flappy-paddles are the same though, and it's important to know which type you're dealing with. With quite a few of the cars equipped with a paddle shifter, you are actually still using an automatic transmission. This is what is generally known as a manumatic, a manually controlled automatic transmission.
This type of transmission still uses a torque converter, which is one of the reasons why this type of transmission is shunned by performance enthusiasts. The other reason is that gear changes tend to be executed very slowly. There is also the F1-derived sequential manual transmission. This type of transmission uses a clutch, so there is no torque converter to sap the power, but it is controlled by a computer. When you tap the paddle, the computer cuts the throttle, disengages the clutch, engages the gear, reengages the clutch and then reapplies the throttle.
This kind of system would allow even less skilled drivers to still have the performance of a manual transmission without having to deal with the difficulties of a third pedal. The problem was, they tended to be very slow. Some of the best (and most expensive) systems would allow for shifts that were genuinely quick, but most sequential manuals had terrible lag and were frustrating to drive. Several automakers, starting with Volkswagen, sought to correct this problem, and have developed dual-clutch transmissions, also sometimes known as a DSG or direct shift gearbox.
The DSG is a bit like having two transmissions at the same time. The two clutches are attached to alternating gears, meaning that the odd-numbered gears have one clutch and the even-numbered gears use the other clutch. The computer can therefore have the next gear engaged before you even select it. Power is then switched from one clutch to the other. Since one clutch can begin engaging before the other is completely disengaged, there also almost no interruption in the flow of power.
This kind of system is not only easier to use but also much faster than it would ever be humanly possible to shift gears using a standard three-pedal transmission. This also gives drivers the option to let the computer automatically shift the gears, giving everybody the chance to enjoy driving with lightning-fast clutch-operated shifts, even if they don't know when those gears should be selected. Even these truly remarkable DSG systems have been slow to gain acceptance from enthusiasts, partly due to the association with inferior types of transmissions.
Also, many drivers (myself included) just enjoy the experience of actually physically changing the gears. The technology behind the DSG is amazing, and there is simply no avoiding the fact that they produce gear changes faster than I ever could. I'm not a racecar driver though, and saving milliseconds isn't vital in everyday driving, and that's good because a DSG still just isn't as much fun.