Grand Admiral Thrawn was introduced into the Star Wars universe in Timothy Zahn's Heir To The Empire novel. He plays a rather major role in the trilogy, and in many other Star Wars novels as well.
Thrawn is an alien, of the race called the Chiss, which hail from the Unknown Regions. They are definitely humanoid, with arms and legs in the right positions and the right proportions, but their pale blue skin, shimmering blue-black hair, and glowing red eyes mark them as distinctly not human.
Mitth'raw'nuruodo, or 'Thrawn' as he calls his core name, first came into contact with the Empire over half a century ago, when Senator Palpatine was setting up an ambush for the Outbound Flight Project. Palpatine's ships were annhiliated, and only one survived because Thrawn wanted to interrogate them. On board the surviving ship was the taskforce's leader, Kinman Doriana, one of Palpatine's top advisors. He persuded Thrawn that the Outbound Flight Project had to be destroyed, and when they arrived in Chiss space, they were. The Chiss thought this was, for all intents and purposes, murder, not believing in preemptive strikes, and Thrawn only just managed to retain his position. He pushed it a little too far in dealing with the Chiss' enemies at one point, though, and was stripped of all rank and sent into exile at the edge of Imperial space, where he was brought back to Coruscant.
As it turns out, Palpatine had made at least two unsuccessful attempts to contact the Chiss and offer Thrawn a position within his soon-to-be-Empire. Thrawn eventually rose to the rank of Warlord, and was given the white uniform of a Grand Admiral, the only non-human ever granted this honour.
Thrawn gained a reputation as a cunning warrior, but eventually he was burnt by the politics of Palpatine's court and sent out on exile to the Unknown Regions on a mapping expedition. This was actually a front, however, for Thrawn to go back to his people. After Palpatine was killed, Thrawn eventually came back and took over what was left of the Empire, using Captain Pellaeon's Star Destroyer Chimaera as his flagship. He unearthed the Spaarti cloning cylinders and the secret of cloaking technology at the Emperor's Mount Tantiss facility on Wayland. He enlisted the help of an insane clone of the Jedi Master Jorus C'Boath, and with the capture of the fabled Katana fleet and Thrawn's military genius and ability to see weaknesses in a species' psyche from merely studying their artwork, Thrawn came extremely close to toppling the New Republic. However, the New Republic's attack at the Bilbringi Shipyards was the turning point. Thrawn was assassinated by his Noghri bodyguard Rukh and the New Republic broke through the shipyard's defences and were rampaging around unchecked inside.
In Zahn's Specter Of The Past and Vision Of The Future novels, Mara Jade and Luke Skywalker found one of the Chiss' bases, which turns out to be Thrawn's work. They find out from the Chiss that are there, who are "Mitth'raw'nuruodo's Household Phalanx", that Thrawn had said if he was ever reported dead, to continue their work in the Unknown Regions and wait for his return ten years after. Mara and Luke eventually found a clone of Thrawn, still in its cloning tank, which explained the "wait for his return ten years after" comment. The clone was killed during their escape from the Chiss' fortress.