Argentina from most aspects is nothing but a big mix of different cultures, and its music is certainly not the exception. However, all this mix is spiced up a little bit and so transformed into what makes it ours.
This is what makes Argentinian music very different from Latin American music, and hence has given our bands and various artists international fame.
However, modern Argentinian music didn't actually take off until the late 80's or early 90's.
Before this(60's and 70's), it was european and american artists who'd flood the markets and radios with their music, and of course there's always the local artists trying to impersonate the big foreign bands.
Even previous to those days (30's-50's), Tango had taken over everyone and everything, and before Tango, it was Old European minuets and walz.
But it was in the late 80's/ early 90's that Argentinian bands broke the mold of Latin American music which consists generally of dramatic solos, like ballads, and decided to include various rythms of different cultures and so come up with our own national style.
Jazz, reggae, blues, flamenco, rock, ska and other styles were mixed between each other, and with our language and culture to create what's known in Latin America as Argentinian Rock. This was one of the first countries in Latin America, if not the first, to "export" our music to the rest of the continent.
Most Argentinians say that the peak of our Rock has passed though, as now the markets are more invaded of American bands and not long-lasting artists.