MATERIAL
Brake caliper material needs to be rigid, light, sturdy and inexpensive. Fans of aluminum can wave your hands in the air-almost all brake calipers are made from the stuff, either cast or forged.
There are some more exotic options for the deep-pocketed and serious race teams though. Magnesium is even lighter than aluminum, and magnesium-alloy calipers are a pricey, yet still practical choice for racing. There's been work done on using metal composite materials in calipers. Metal matrix composites use strands of carbon fiber suspended in aluminum, and in the future could make for an even lighter brake caliper.
CONSTRUCTION
The ideal caliper construction is the "monoblock" design which is, as the name suggests, made from one piece of metal. Clever tools cut out the hollows for the pistons and the channels for the hydraulic fluid from the inside of the caliper clamshell. This is expensive though, so most calipers are made up of two halves bolted together. These are much easier and quicker to machine and therefore cost less. The disadvantage is that they are less resistant to flex under load, so they waste more braking effort and reduce 'feel' through the lever.
Three-Piston Sliding Used...
Three-Piston Sliding
Used on Honda's CBS brake systems on the Super Blackbird and VFR800. One piston on each caliper is linked to the rear brake pedal.
A halfway house is to machine the piston bores from the outside of a monoblock caliper casting, then use a plug to close the outside holes up once the caliper is assembled. The blue, silver or gold centered Sumitomo calipers on Yamaha R1s, R6s and FZ1s use this technique, which falls between a pure monoblock and a two-piece caliper in terms of cost and complexity.
MOUNTING CHALLENGES
Most current sportbikes use radial mounted calipers, where the mounting bolts are arranged radially in relation to the wheel axle-parallel to the wheel spokes. This method has taken over from the 'traditional' mounting method, where the bolts are arranged parallel to the wheel axle, and it has a number of advantages.
Having the caliper mounted at each end makes a radial mount stiffer, and keeps the pads aligned more precisely. It also uses the bolts in a better engineering sense: a conventional mount has the bolts in a 'shear' position, which places more stress on the bolt shank than a radial mount. Radial mount bolts are used in a 'tension' position on the caliper bracket, which means they are under less stress and can therefore be lighter.

Dual-Piston Sliding Used...

Dual-Piston Sliding
Used on small capacity roadsters like Kawasaki's Ninja 650R and Triumph's Street Triple. Also seen as a rear brake on large tourers and cruisers.

Four-piston opposed Most...

Four-piston opposed
Most common supersport brake design.

Eight-piston opposed Rare:...

Eight-piston opposed
Rare: seen only on Buell's 1125R and CR.

Single piston sliding Used...

Single piston sliding
Used as a front brake on scooters and small commuters. Mostly seen as A rear brake on supersport bikes.

Six-piston opposed Used on...

Six-piston opposed
Used on Yamaha's 2009 R1 and V-Max.

Yamaha's "semi-monoblock"...

Yamaha's "semi-monoblock" caliper saves money in production yet offers improved performance.