The chain on a bike transfers the power created from the pedals of a push bike to the "drive-wheel", and in turn propels it forwards.
The roller chain with a half inch pitch is the chain in use on modern bicycles.
Practically all modern bike chains are the 'Sedis bushingless' design as it allows good flow of lubricant within the rollers and provides good lateral flexibility, as well as being cheap to make.
The block chain, skip-link chain, and Simpson lever chain are examples of earlier bike chain designs which are now virtually obsolete.
Current popular manufactueres of chain rings include Campagnolo, Rohloff AG, KMC, Shimano and SRAM.
The first bicycles didn't have metal chains at all, and had the pedals fixed straight onto the front wheel - resulting in designs of bikes with very large front wheels, due to the top speed being directly proportional to the diameter of this wheel.
The introduction of chain drive permitted the drive plus the sprockets to dictate the top speed, thereby allowing the circumference of the wheel to be decreased dramatically for safety - hence the bike then produced being known as the 'Safety Bicycle'. The introduction of the chain also permitted the further development of gears, allowing riders to adjust the gears depending on the terrain they are cycling over.
A chain must stay lubricated to work effectively, however it is difficult to find a lubricant that both pentrates the chain, but also stays clean. You must never lubricate a dusty/dirty/muddy bicycle chain as this can push the dirt particles further amongst the rollers. You should always clean a chain before lubricating it, and you can get small devices/containers to help you do this. Some bikes have chain guards so as to protect the chain from getting dirty, and cutting down on the maintenance required.
Chains can wear out or stretch, which then can make changing gear and cycling a problem. You should replace a worn chain before it causes wear to the rear sprockets and chainrings too.