Formula One racing is really two races happening at once, one fast and one slow. The fast race is the one you'll watch on TV or in person, and the slow one is the race between technological development and the rules.
A modern F1 car can accelerate to 62 mph in less than two seconds, pull more Gs than a Space Shuttle launch, and hit a top speed over 200 MPH in qualifying.
Formula One organizers in the 1970s decided that maybe it'd be a good idea to try and kill off less racers and since then there has been a continual battle between the race car builders and the race organizers. The car makers and drivers are all trying to make the fastest car possible, and the officials are desperately trying to keep speeds reasonable and safety standards high.
As a result, the modern F1 car is a fascinating mix of cutting-edge technology and heavily-regulated mainstream technology. The engines are a great example. F1 used to allow turbocharged engines, but engine makers were making insanely powerful engines— in some cases around 1000 HP. To curb this trend, 2012 rules stipulate only normally aspirated 2.4 L V8 engines, with only four valves per cylinder, and made of non-exotic materials.
At first glance, this sounds a lot like a smaller version of the V8 you could find in many cars— until you realize that F1 engines routinely rev up to 18,000 RPM. Thanks to all those revs, they produce about 300 HP/L for a total output of around 750 HP or more. Each team gets eight engines to use over 20 races.
Because of all the restrictions, every part of an F1 car has to be the lightest, strongest, most aerodynamic, and best component it can be. The exotic aerodynamics of the car have to balance wind resistance while maintaining enough downforce to keep the power to the road. Until it was made illegal this past season, teams would design cars that vented their exhausts strategically over aerodynamic surfaces to apply more downforce without increasing drag. This year, teams can have dynamically adjustable wing surfaces and some teams are experimenting with flexible nose assemblies before they likely get banned as well.
I made a chart explaining both the regulations and the resulting tech of the F1 cars out there. You can expand the chart and print it out, so you can use it as a handy placemat for your snack table during the race, and provided you can wipe away the mustard and beer, refer to it during the excitement. You're welcome!