Today, intellectually disabled athletes can participate in a variety of international sports competitions. For an athlete, access to one or another of these events is possible according to their level of sporting ability or their intellectual capacity, but also depends on their country and the extent to which it hosts International Sports movements. One option for those who have the greatest sporting achievements – and often the greatest intellectual capacity – is to be involved in the competitive circuit organized according to the pyramidal logic of traditional elite sports and in which the ultimate aim is participation in the Paralympic games, a greatly valued perspective that epitomizes a process of de-stigmatization of these athletes. Everyone can participate in an international sports event and ‘play at’ being champion by committing to the Special Olympics movement, which offers particular and non-selective sports games, but which does not command the same recognition or the eventual de-stigmatization.