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 pressurised air to an engine.
Why?
The main performance advantage is to have boost at lower revs and aid the spool up time of a relatively large turbo charger thus eliminating turbo lag. This also makes a twincharger system very streetable compared to a drag or dyno queen turbocharged system.
A street car can benefit from better economy and emissions with a smaller capacity engine than a comparable power naturally aspirated engine due to alot of driving done off boost, ie cruising or sitting at traffic lights.
Application ?
Most beneficial in sprints, motorkhana's, hill climbs etc where stop/start racing is required. Or a small capacity large turbo street car for those who can't get enough. There are limited benefits for track racing purposes... where constant high speed and rpm make a turbo system the better option.
Which system?
Compound or Sequential? turbo into super or super into turbo? pre or post supercharger throttle? one or two intercoolers? There's more than one way to setup a twincharger. (more info to come).

Challenges with the twincharger system:
* Designing a system that is not overly complicated.
* Cost- All those extra parts, fabrication, time, labour, design, tuning... is the extra cost worth the benefits gained?
* Controls- If sequential system is used, correct bypass valve control is most important for smooth operation.
* Size- Compact it all into one engine bay.
* Heat- More boost and power means more heat created. therefore a need for better cooling requirements.
More engine parts and piping means less engine bay space. less air flow through the engine bay and more heat sink.
*Weight- Extra weight is undesirable in any performance oriented car. Suspension and braking could also be affected by the added weight.
* Tuning.. any high performance highly boosted engine needs accurate tuning for safe and reliable running.
* 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
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