Probably the most influential composer in the tango genre, and one of the most important composers of the 20th century to begin with, was Astor Piazzolla, who studied with Nadia Boulanger in Paris. One of his crucial contributions has been to register the tango on the map of 'serious' music, through his originality and the depth of his compositions. Prior to Piazzolla, the tango wasn't considered 'serious' music, and the bandoneon was not considered a relevant instrument in the classical repertoire. He changed all that, single-handedly.
Of the period when he studied with Boulanger, who trained many contemporary classical composers, Piazzolla writes the following:
There's a (probably apocryphal) shorter quote that goes something like: "You can choose: you can either become a mediocre Bartók - or you could be the best Piazzolla the world has ever seen."