Almost nothing is known about Rasputin. He has based his superhero identity on the historic figure, but is otherwise a shadowy, mysterious figure. He lives in a small fortress in the Ukraine, with a genetically altered bear, and does research on genetics and computer technology for the government.
It is implied, albeit ambiguously, that he really is the legendary Rasputin, back from the dead. Especially considering that it is never revealed if he died in the explosion of his fortress or if he escaped.
After Dr. Kremlin was successfully created, Rasputin knew that there would be others trying to follow suit. He contacted all of them secretly, and proposed a meeting at his base. Problems arise, though, when none of the heroes can agree on what path of action would best benefit the Motherland. Propaganda is far too concerned with eastern Europe and loyalties at the edge of the Iron Curtain, while Proletariat is eager to help Japan and hit the US and Canada hard and fast. Meanwhile, Cossack-Owl and Silk Shadow are both too wary of the impact Dr. Kremlin will have on the Russian People, and Kremlin himself is mostly unconcerned with the present situation, wishing to directly speak with Dr. Manhattan.
In the end, Rasputin takes control, and decides that the best course of action for everybody would be to have Dr. Kremlin start advancing into the Middle East and western Europe as soon as possible.
This same meeting is referenced in flashback form in Red Sunrise, from Kremlin's perspective. In this version, Rasputin can't calm the other heroes down, and Proletariat ruins the meeting.
Encounter with Manhattan
Shortly before the invasion can begin, Rasputin's fortress is compromised by a joint effort by Inkblot, the Comedian, and Nite Owl. Propaganda is seriously injured in the fight, but not before he can fatally wound Ben Kovacs. Proletariat and the Silk Shadow capture the Comedian, and Nite Owl is forced to use the Manhattan Signal to call for backup.
Rasputin tries to stop Dr. Manhattan with a tachyon-coated scimitar, but gives up when Manhattan tells him that Dr. Kremlin has been killed in Afghanistan. Furious, Rasputin triggers several explosives based on Kremlin's energy signature, and brings down the fortress around him. Manhattan takes Nite Owl and Ben's body back to New York. The Comedian, Proletariat, and Silk Shadow escape to the southeast, and remain in hiding until the .
Ozymandias Jr. mentions having had multiple encounters with Rasputin, at least one of which has to take place after the Red Star storyline, but there are absolutely no other traces of the character. It has been suggested that the writers were saving him for a final crossover event, but, unfortunately, the series was canceled before that could come to pass.