A fixed gear bike (also referred to as "fixed-wheel" or "fixie") does not have a freewheel mechanism, it does not allow the pedals to stain stationary when the bike is in motion. You cannot coast on a fixie, you have to be always pedaling to keep moving. The drivetrain is coupled directly to the wheel - this allows the rider to effectively control acceleration and braking using legs and bodyweight.
Fixed gear bikes have been a standard in track racing and are becoming more and more popular among urban commuters worldwide - these bikes are very lightweight, technically very straightforward and give the rider amazing control.
Apart from velodrome track racing, fixed gear bikes are now being raced in the Criterium race series. This race takes place in the streets, one of the events is held in New York - Red Hook Crit.
A new format for fixie racers that is becoming more and more popular in Europe is "Last One Standing" promoted by 8bar. The idea is that every run eight riders start and every two laps the last rider is kicked out until only four riders are left. In the finals the same scheme applies until only one rider is left who becomes the overall winner of the race. Next event is taking place at the Berlin Velodrome in January 2022 so if you are there - check it out!
Check out this very cool video from the 2015 EVENT!