The article has two basic aims: to review the paradigms that have been proposed in the post-war scientific debate to understand the Italian mafia phenomenon; to propose a new interpretation of the mafia which is based on the declarations of former members of the two largest and most stable Southern Italian mafia associations - the Sicilian Cosa Nostra and the Calabrian 'Ndrangheta. This new interpretation may be summarised as follows: mafia sodalities are neither bureaucracies, nor enterprises, nor an industry of private protection. They are, instead, secret, multifunctional brotherhoods. Founded on what Max Weber called "contracts of fraternisation", over the past hundred years they have used the strength of associative bonds to pursue extremely different ends and carry out the most various functions. Among these, a very important one has always been the exercising of political dominion. The very resources - the paper argues - which have fostered mafia associations' longevity and success also represent powerful constraints on their current evolution.