Inside a viscous coupler as shown in the right hand side picture, there are many circular plates positioning very close to each other. Both drive shafts connect to roughly half of the plates in an alternating sequence as shown. The sealed differential housing is fully contain of a high viscosity liquid, which has a strong tendency to "visco" those plates together.

In normal condition, front and rear axles run at roughly the same speed so the plates and viscous liquid are relatively stable to each other. When tyre slip occurs in one of the axle, that means the alternating plates run at different speed, viscous liquid will try to visco them together. As a result, torque is transferred from the faster driveshaft through the liquid to the slower driveshaft. The greater the speed difference, the larger the torque transfer. As a result, limited slip function is implemented.

Characteristic of Viscous Coupling center differential
Note that Viscous-Coupling LSD is a speed-sensing device: under no-slip condition, no torque will be sent to another axle. Whenever slip occurs, theoretically up to 100% torque can be sent to any axle, depending on the traction difference between front and rear axle. Therefore it is a part-time 4WD.
Being a part-time 4WD, it does not have the neutral steering of a permanent 4WD can obtain. For cars based on rear-wheel drive models, such as Porsche 911 Carrera 4, this is not a real problem - as normally the car runs like a RWD car thus is capable to deliver the desirable throttle oversteer . However, for other front-wheel drive-based cars like VW Golf Syncro and Volvo 850 AWD, the part-time 4WD can do nothing to correct their understeering manner. This is the first disadvantage.

The next problem is the delay before the 4WD get into effective. Since viscous liquid is not a fixed medium (unlike gear), it takes time and speed difference to be effective. The function between speed difference and torque transfer is an exponential function - that means in the early stage of slip, torque transfer remains near zero.

To cure this problem, most manufacturer varies the final drive ratio such that introduce a slightly speed difference even in normal condition. As a result, the car actually runs with 95:5 torque split between front and rear. This shorten the delay time. However, it is still impossible to match the pure mechanical Torsen LSD.

It might be less effective than Torsen system, but it is certainly the cheapest, so we can find it in many mass production 4WD cars.
Advantage: Cheap and compact
Disadvantage: Part-time 4WD only. Normally feels like 2WD.
Who use it ? VW Syncro, Lamborghini Diablo VT, Porsche 993/996 Carrera 4 and Turbo, Volvo 850 AWD etc.