[6][7] The association is responsible for the organization of the world's major quadball tournaments and events, most notably the IQA Global Games, as well as international rule setting and worldwide expansion.

Quadball, then known as "muggle quidditch", began in 2005 as an intramural league at Middlebury College in Vermont.

In July 2022, the IQA announced plans to change its name to the International Quadball Association, attempting to re-brand the sport, both to avoid future confrontation with Warner Bros. Entertainment over their trademark of the term "Quidditch", and to distance the sport from J. K. Rowling due to her controversial statements about transgender people.

As of 2022 these are: Under the IQA, there can exist groups of NGBs that work together to form a committee devoted to promoting the sport within the region.

[12] However, this policy has drawn sharp criticism from single sex institutions for whom it is difficult or impossible to attract players of the opposite gender.

July 2012 saw five national teams from around the world compete in this first international tournament run by the IQA, taking place in University Parks, Oxford, England.

[14] The IQA European Games is the regional tournament held every off-year alongside the World Cup.

The inaugural Games were held in Sarteano, Italy in July 2015 which saw 12 nations compete with France being the winner over the UK.

2014, the last year the World Cup in this function was held, saw all European teams refuse their bids due to costs and desire to support a more international IQA with their attendance at the Global Games.