Hooded Justice's origin is never revealed. There are many hints throughout the book that he is in fact Rolf Muller. None of the characters in Watchmen ever saw his face with the exception of Captain Metropolis. He was a member of the Minutemen. Tension soon grew in the group after Edward Blake (The Comedian) attempted to rape Sally Jupiter (Silk Spectre). The rape attempt was prevented by Hooded Justice and in his anger he attacked The Comedian. During the beating, the Comedian mocks Hooded Justice saying he enjoys beating people and is sexually aroused by it, eventually forcing Hooded Justice to stop.
It is implied that he was in a homosexual relationship with Captain Metropolis. During the scene in which Laurie Jupiter and Dan Dreiberg were having dinner, Nelson and Rolf could be seen holding hands in the foreground. They covered up the relationship by having it appear as though Silk Spectre (Sally Jupiter) was Hooded Justice's girlfriend. Like Hooded Justice's identity, this was also never fully confirmed.
After the Minutemen disband, Hooded Justice is suspected by the government to be a Russian agent, forcing him to go underground and disappear. Later a dead body supposedly belonging to former circus strongman Rolf Muller is found. There is speculation that Hooded Justice and Rolf are the same person. It has been said that Rolf was a communist agent but this is unconfirmed. Ozymandias stated the Comedian was sent after Hooded Justice, however the Comedian failed. Ozymandias theorized that Blake found Hooded Justice killed him and reported failure. Ozymandias' theory contradicted the scene in the restaurant.
In actuality, Hooded Justice is implied to be Josef, a young, blonde adolescent boy imprisoned in the same orphanage as Silhouette. It's implied that his victimization at the hands of Rolf Mueller led to his development as a sadomasochist and may have led to his adaptation of the black hood. The Silhouette became obsessed with exposing him as Mueller who had changed his name and moved to the US in the guise of a circus strongman in order to continue preying on children. Eventually going into hiding during the HUAC hearings and with The Comedian trying to expose him. He was framed by Comedian and killed by Night Owl when he broke his neck in a fit of rage, believing that he had killed Silhouette and framed Liquidator for the crime. His body was then destroyed when Captain Metropolis blew up the old Minutemen headquarters, the tragic truth remaining a secret between Night Owl, Metropolis, and Comedian.
As mentioned in Hollis Mason's Under the Hood, hooded Justice has expressed approval for Hitler's actions during the Third Reich. This further links him to Muller. This makes him hypocritical considering the Nazi's attitude toward homosexuals. It is also implied by The Comedian that he likes giving and taking pain, making him a sadomasochist.
Though he (like many characters in Watchmen) had no powers, he was very strong and skilled. Again alluding that Hooded Justice was a strongman or a weightlifter outside of his vigilante endeavours.
Design-wise, he resembles Black Hood and Hangman. This is possibly intentional.
Hooded Justice appeared in the Watchmen movie. He spoke with a German accent alluding to the theory he and Müller are the same person.