Founded in the early 90's by Gen Fukunaga as FUNimation Productions, it rose to anime distribution prominence through one of it's first major properties, Dragonball. After showing Dragonball Z on Cartoon Network back in the late '90s, they became a familiar name to most anime fanboys and fangirls.
They were acquired by Navarre Corporation in mid-2005, and their name was changed to FUNimation Entertainment.
FUNimation is often criticized because of its rather unfriendly relationship with the fansubbing community, the low number of episodes on high priced DVDs (I remember when I was a young otaku, and had to pay $40 for a dubbed VHS tape with only 2 episodes), and the fact that they are the guys who release DB/DBZ/DBGT.
On Saturday, July 22nd, 2006, at the San Diego Comic Con, Harmony Gold announced that FUNimation has the Television, Theatrical, and Home Video rights for Robotech: The Shadow Chronicles.