The Italian-Argentine immigrant Astor Piazzolla rose out of the NYC slums to become the world's most noted avant-tango composer, fusing the traditional with classical, jazz and (later) electronics. He was a standing-up master of the bandoneon, but could also play piano.
He heard jazz while growing up in NYC, but still loved tango orchestras and studied classical. One of his heroes, the great tango bandleader Carlos Gardel, was impressed enough with Astor's chops that he asked the 13-yr old to join his orchestra for a tour but Piazzolla's father refused to allow it. Of course, it was that very tour that killed the entire Gardel band in a plane crash.
He went on to form a unique chamber music ensemble to play his compositions, disregarding the massive criticism from the purists. Some concerts saw audiences reacting with violence. From the mid-'50s onward, his music became increasingly experimental with jazz improvisation, dissonance and electric instruments.
Until Piazzolla, the tango usually accompanied dancers and vocalists. He succeeded into turning it into a high artform. His style was perfect for films, of which his music supported many. He collaborated with Gerry Mulligan (one of his influences), as well as Kronos Quartet and also wrote for symphonies. His late quintet music is worth the hype. In my opinion, his music is some of the most exciting I've ever heard.
Here's his 1986 classic, Tango: Zero Hour: