One of the oldest track cycling disciplines.
You're sitting blankly watching the Olympics on the box, as one does. On the screen are two cyclists in the velodrome, locked in an apparently mortal struggle to get the other to go in front. They come to a dead stop and stay there for half a minute. Your mum walks in and sees the two stationary riders: "What are they doing, then?"
The cycling match sprint is a contest between (ideally) just two riders over a few laps of the track; the canonical distance is one kilometre, but it will be rounded to somewhere between 2 and 5 laps, depending how big the track is. Riders draw for positions and may receive a push start; unlike any other form of sprinting I know of the start is not particularly important. There are no starting gates, no countdown, just a whistle when both riders are ready.
The sprint distance is a fairly carefully selected one from the point of view of physiology. A world-class rider can knock out a standing-start kilometre time trial (itself an Olympic and World Championship discipine) in just on a minute, more or less comparable to the 400 metres for a runner, effectively just beyond the limits of anaerobic performance. That fact, combined with the relatively high drag coefficient of a cyclist and the absence of separate lanes for the riders, means that a rider who attempts to go flat out from the start is likely to do nothing but give their opponent an easy ride in their slipstream until they make their final attack in the closing 200 metres or so. Therefore it is in riders' best interest to be behind the other guy until the last possible moment - hence the cat-and-mouse stuff that goes on in the early stages.
It is still possible to win from the front, however; assuming you cannot do it on raw speed alone, the trick is to shake the other rider off your tail, feinting and timing your attack to surprise them and open a gap they cannot close. It is entirely legitimate to use the entire width of the track and to take advantage of the banking to increase your acceleration; you can pass your opponent on either side unless they are inside the "sprinter's line", about a metre out from the inner edge of the track; once into the final 200 metres (which are usually timed, although more for interest than to determine any placings) you are required to hold your line to prevent the front rider from merely blocking all the way to the line. Nonetheless, sprinting remains something of a contact sport and a certain amount of intimidation - leaning down on your opponent, or feinting a flick to keep them wide as they try to pass - is de rigueur (and it is not unknown for the odd punch to be thrown). The advantage of a rider coming from behind in the closing stages is also slightly mitigated by the fact that they will have to come further around the outside on the final banking; holding your opponent as far up the track as possible (without letting them nip through on the inside) is a useful tactic.
In earlier times there were no limits on the delaying tactics, but after entire meetings' schedules were disrupted when riders held 45 minutes trackstands some restrictions were imposed, first with the match being restarted if a trackstand lasted more than a couple of minutes, and latterly by (a) requiring the riders to ride at walking pace or more for the first lap (the rider drawn on the inside of the track has to lead unless the other rider passes voluntarily) and (b) tightening up on the definition of a trackstand by making it a disqualification offence to actually ride backwards at any stage (defined as a backwards movement of more than about 10 cm - you usually hold a trackstand on a fixed wheel track bike by rocking fore-and-aft, so this makes it harder to maintain; hopping your bike sideways to improve your launch angle down the banking and skipping your back wheel to get the pedals ideally placed for a starting lunge are also harder than they once were).
Sprint tournaments today are normally seeded by a time trial qualifying round over 200 m with a flying start; the qualifiers then ride a single leg in early rounds with losers going through a repechage for a second chance until the quarter-finals, at which point it moves to the best of three matches until the final. First round and repechage matches and minor finals are often run off with three or even four riders, which changes the dynamic somewhat; they are generally fairly quick affairs. In more lucrative but less serious moments, the top sprinters often perform in exhibition matches in conjunction with six-day races and other meetings, although they are not the hall-fillers that they were up to the 1950s.
Until recently tandem sprinting - a spectacular affair, usually decided by two falls or a knockout - was also practiced (usually over 2000 metres), but dwindling interest sadly led the UCI to drop it as a World Championship event after 1994. Tandem racing persists as a Paralympic discipline for riders with visual handicaps partnered with sighted ones, providing the odd circumstance where an able-bodied athlete can win a Paralympic medal.
Track sprinters are something of a breed apart from other cyclists, although the kilo and the keirin have given them some extra racing; the routier-sprinters who dominate bunch finishes in road racing are more akin to track pursuiters in physiological terms, winding up over several kilometres. It is not entirely surprising that in quite a few cases sprint coaches have also been involved in the world of boxing.
The track sprinting greats: Major Taylor, 'Poeske' Scherens, Reg Harris, Arie Van Vliet, Daniel Morelon, Gordon Singleton, Koichi Nakano, Florian Rousseau, Felicia Ballanger, Arnaud Tournant, Chris Hoy, Gregoire Baugé, Victoria Pendleton, Anna Meares.