(This was written in response to a friend asking me to explain Track Racing during the Olympics.)
About a hundred years ago, bike racing was bigger than unsliced bread. Since every race widow knows that nothing is worse than watching an outdoor bike race pass by once every 45 minutes, people decided to hold these races indoors. It also had the benefit of exposing racers to second hand cigar smoke, which improved their constitutions. Gravity had recently been discovered, and to offset its effects, the banked track was developed.
Dr. Jonas Salk invented amphetamines, primarily used to fuel "six day" bike races, in which competitors rode in circles until nearly all of them died. If spectators got bored, they could watch a 45 round bare-knuckle prizefight on the infield. It was the Golden Age of American Sport.
At some point, civilized people decided that was not a very effective way to kill people, so they invented World Wars, and Six Day Races declined in popularity. Race promoters decided to complicate Track Racing so people could bet on it in new ways.
Before we get much further, it's very important to understand there are two primal types of Track racer: Sprinters and Endurance riders.
Pure Sprinters are actually just weightlifters that have learned to stay upright on two wheels. If you believe the scientists, it's because they have a high number of fast-twitch fibers. Creationists believe they were just born with the legs of a mule.
Everyone else is an Endurance rider. They hate Sprinters because Sprint training consists of hanging around the weight room, eating slabs of chocolate cake, and taking a nap. Then they go to the track and ride for 30 seconds, and rest for an hour. They repeat this 3-5 times.
Endurance riders are not to be confused with your typical Tour de France road racer. A track Enduro - as they call themselves because it sounds tough - goes much faster than their road counterpart. However, it's largely a result of the fact that their bikes that cost about as much as a year of college. Only in Track racing does four minutes count as lasting a long time.
Nonetheless, all of Track racing is set up to make the Sprinter-types face off against the Enduros, in a variety of schemes to keep race officials employed:
Match Sprint
Strictly for the pure Sprinters. It's a three lap race, which about two laps longer than they'd like, so they slow it down and eyeball each other. It's like a game of Chess, which is what people say about a really boring boxing match where neither guy throws any punches until the third round. They all know each other's weaknesses pretty well, so they play games, trying to jam up the other racer, or slow down the race, or escape, etc.
Pursuit (Individual or Team)
Strictly for the pure Enduros. Racers start at opposite points on the track, and try to catch one another, or just finish with the best time. It's more or less a time trial, but since those are about as exciting as watching paint dry, they double the fun and run two at once. It's still pretty boring, unless you're the type who owns multiple skinsuits, and you can tell which one makes you faster.
Keep in mind that only a handful of people are pure Sprinters or Endurance riders, most everyone else is somewhere in between, but they have their natural tendencies that the others want to exploit. The Sprinter types will drop out of any race longer than six laps, but on the way out, they will casually mention their other accomplishments like "I guess I shouldn't have squatted 800 pounds this morning." The Endurance riders are like "lol ur so fat."
The Scratch race
First one to the finish line wins. This sounds straightforward, but it gets complicated. The Sprinters think "let's keep this friendly until the last lap or so" while the Enduros are like "hey look, free cheeseburgers" and they try to escape and get a lap ahead.
Every other race is contrived to get them all to beat the crap out of each other, mostly by putting lots of sprints in races of various lengths. Sometimes the Sprint types can hang in and keep the group together, usually the Enduros try to escape so they only have to sprint against each other. The ones that can't sprint at all try to run off solo, but if they have to sprint, at least it's only against some other racer with arms like sticks of spaghetti. Not all of these events are in the Olympics, but they include, among others:
Points Race
A generally long race, with points awarded four places deep, usually every 10 laps. The losers can go home and brag "yeah, but at least I won the third sprint in the second race."
Point-a-lap
Like a mini points race. This is one of the races where you can suck 65% of the time, finish a lap down, but somehow win.
Tempo
Like the Point-a-lap, but the first racer across the line every lap gets two points, the second racer gets one, and nobody else gets squat. Rewards racers that can keep an eye on who's winning while their heart rate is in cardiac arrest territory. Another race where you can lose every sprint and still win.
The Madison
A race in which two riders take turns racing, while the other slow rolls it around the track. They replace one another in the racing action by swooping down from the banked turns and hand-slinging one another up to speed. Half the time, even the officials don't know what's going on, but, like NASCAR, everyone loves it because it looks like there will be a deadly crash at any moment.
Keirin
Someone got the idea to use a motorbike to get the Sprinters going pretty fast, since they would never work hard enough to do that on their own.
Miss 'n Out
Last one across the line every lap gets pulled. The Olympics calls this the Elimination race, probably because its other name, "Devil takes the hindmost" just sounds dirty.
The Omnium
Some combination of events, for people that can't do any one thing well.
It all adds to a bit of mayhem sometimes, but for the most part, it makes for amazing racing because everyone is trying to take everyone else apart all the time, and it's brutal, and fast. Every once in a while, you get to see a little exasperated hand waving, which is a Track racer's way of saying to the official "I was about to uncork my big move but that guy cost me the race." In reality it means they were pretty much beaten at that point, but sometimes it works.
