The ubiquity of randomness and the consequent need to understand random phenomena in order to make adequate decisions led many countries to include probability throughout the curricula from primary education to University level. This need was also recognized by the mathematicians who developed the probability theory. This is a relatively young field, and is not free of controversies, which are also reflected in the lack of agreement on a common definition of randomness. Psychological and didactical research, suggest widespread misconceptions and misperceptions of randomness; however, these results have not always been taken into account in teaching, where randomness is considered a transparent concept.