When smoked (not as in ganga) common carp tastes like almost any other smoked fish, although seems to be seasonally more muddy flavored at times, or if taken from turbid rivers. The carp from large clear mesotrophic, or or oligotrophic lakes like Michigan or Superior are really good eating, and can get 4-5 ft in length, although most probably average 3 ft. I would see lunkers jet past when scuba diving on or slightly below the thermocline.
I believe they were intentionally introduced from China back in the 1800s as food fish. In those non eutrophic lakes, they thrived, but didn't overpopulate because of the lack of vegetation .
In the last decade one of the most destructive introductions have been the brown goby that came in in the bilge of Asian container ships, where they have taken over the near shore habitat edging out native species like sculpin, and eating the spawns of bass and other game fish.