Who's This? The animal-headed threesome on page 23 of Who's Who vol.XXIII.
How you could have heard of them: In Matt Wagner's Doctor Mid-Nite mini-series, they were responsible for causing the hero's day blindness, fighting G'nort in GLC Quarterly #5, and more recently appeared in Detective Comics #832 and wound up in Arkham Asylum. They've also appeared in three Batman animated series - BTAS, The Batman, and Brave and the Bold (the one with Bronze Tiger).
Example story: Detective Comics #253 (1958) "The Fox, the Shark, and the Vulture" by Dave Wood and Sheldon Moldoff
I'm actually surprised the Terrible Trio didn't appear more than it did. After all, thematic crimes are Batman's bread and butter. Maybe the alliterative name made some writers think they were actually terrible. Maybe their individual names were appropriated by other characters, both at DC and elsewhere. Maybe the band just broke up. I don't know. But I think they would have made interesting crime lords in later eras.
Who else? Thriller might have been next, but I reviewed the whole series as part of my Old 52 feature. But we are going to do a team next.