What is the polka dot jersey in cycling? (or Tour de France)

The polka jot (aka King or Queen of the Mountain) jersey is used by both the Tour de France and La Vuelta grand tours to denote the rider who is currently in the lead of the King of the Mountain (KOM) classification. La Vuelta's polka dot jersey, instead of being white with red dots is white with blue dots. The other major grand tour, the Giro d'Italia, uses a blue jersey, the Maglia Azzurra to denote the current KOM classification leader.

The polka dot jersey is often used by other smaller stage races throughout the year to denote the current KOM classification contender but there's no standard across the board and each race is open to choosing the color of jersey that works best for that race.

As like all classification jerseys (eg. white, yellow, green) the winner gets to keep the jersey and corresponding kit that goes with it for the rest of their careers. So simply holding it for one day is a goal of many professional cyclists.

Points in the classification are awarded on reaching the peak of the categorized climb ahead of other competitors. Points are doled out often in an exponential fashion similar to F1 and race positions.

So for example a category two climb may offers points to the top five competitors who cross the summit first. The rider who is first may receive 10 points, the second rider six points, the third rider four points, the fourth rider two points, and the fifth rider one point.

If the climb was a category one climb (harder) and not a category two climb there may be points for the first eight (instead of the first five) over the summit and the points may start at twenty instead of ten.

The points awarded are not static and changes year to year and event to event. Race directors are always tinkering with the awarded points to attempt to make the most exciting race and a contested classification.

Bonus points were in the past given to climbs that bookended a stage, but that has started to be phased out as race directors realized that doing so led to the main general classification contenders also always winning the polka dot jersey on top of the leaders jersey.

Why would they win both? GC contenders need to win stages for both bonus seconds and battle their contenders on hilly finishes. Given those hilly finishes that they often win GC contenders are always close in contention for the KOM jersey.

Fun Factoid. The KOM Jersey has never been held by a single rider from start to finish of the Tour de France.