Twin Charge, Twin Charger, Twin Charging, Twin Charged, Super Turbo, 4agze 4agte 4agzte 4agtze
What is it?
Using a super charger and a turbo charger to provide compressed air to an engine.

Why?
The main performance benefit is the combination of advantages of both charger types which also compensates for the disadvantages of each. This provides a broad torque band and great top end power. Instantaneous boost from lower revs from the supercharger aids the spool up of a relatively large turbo charger thus eliminating turbo lag and potentially providing top end power usually only seen on dyno queens and drag cars. This also makes a twincharger system quite streetable in comparison, if traction can be maintained :)
In a street car, they can benefit from better economy with the smaller capacity engine than a comparable (in power) naturally aspirated engine due to the majority of driving time being off boost, ie cruising or sitting in traffic. Emissions can be acceptable by starting out with a modern engine design and incorporating as many of it's emissions improvement features as possible (direct injection etc) so long as they don't hamper power when it's required. This wont happen without the ecu being tuned in the low load areas to improve emissions and efficiency.

Application?
Most beneficial in sprints, motorkhana's, hill climbs etc where stop-start racing is required. Street use can be potentially unpractical and unsafe if the vehicle is over powered. Track racing has limited benefits, where constant high speed and rpm make a turbo system the better option.

Which system?
Compound or Sequential? turbo into SC or SC into turbo? throttle pre or post supercharger? one or two intercoolers? poppet, butterfly or flap bypass valve controlled mechanically or electronically? There's more than one way to setup a twincharger.

Challenges with the twincharger system:
* Designing a system that is not overly complicated.
* Finding a garage/workshop that understands the system and capable of repairs, maintenance and tuning if not able to DIY.
* Cost- All those extra parts, fabrication, time, labour, design, tuning all add up. Is the cost worth the benefits gained?
* Controls- If sequential system is used, correct bypass valve control is most important for smooth operation.
* Size- It all needs to fit into one engine bay without restricting airflow. Space restrictions can often determine what system is used.
* Heat- More boost and power means more heat generated. therefore a need for better cooling requirements.
*Weight- Extra weight is undesirable in any performance oriented car. Handling and braking could also be affected by the added weight.
* Tuning- Any high performance highly boosted engine needs accurate tuning for safe and reliable operation.
* Reliability- More parts, more heat, more power, more stress, more things to go wrong.

Non Intercooled Supercharger system in RWD layout
Notes: Probably the simplest setup in terms of parts and plumbing using a sequential system and one intercooler. A water/meth injection system could aid cooling requirements of intake air temp.

Main parts required:
turbo
turbo exhaust manifold and dump pipe
turbo oil feed and drain
external wastegate and plumbing (if not running internal wastegate)
supercharger
supercharger mounts, pulleys, belt, tensioner
electromagnetic clutch for supercharger
supercharger controller (to switch on and off)
bypass valve (and bypass controller) or one-way valve
boost controller
plumbing everything together
intercooler and bov
programmable ecu
beefed up fuel system, bigger pump, injectors etc
stronger engine internals, stronger drivetrain, bigger brakes... how fast do you want to go?

Useful links:
Notes on the AW11 4agze supercharger
Eng-tips.com twincharger discussions (madmac and warpspeed)
wikipedia twincharger info
autospeed ae92 HKS Twincharger article
autospeed Nissan Super-Turbo article
4agzte datsun 1200
Twincharging - Concept & Example application
Autozine.org Lancia Delta S4 twincharger info
Shalco Motorsport Lanca Delta S4 twincharger info