He was reelected in 2002, 2006, and 2010, serving four terms. The attackers were not found but two policeman were charged as accomplices because they did not do anything to help Révész at the time he was attacked. They were convicted in April 2011 to one year in jail, the sentence was suspended.
After the Fall of Communism in Hungary he entered the local government of the 10th district of Budapest shortly after the first free elections in 1990. In 1991 he became the chairman of the local Fidesz chapter in the same district. On 23 October 2006, during the protests against the Socialist government, he was attacked while trying to mediate between police and a crowd during the Gyurcsány cabinet.
He was first elected as a member of the Hungarian Parliament in 1998. Révész was a member of the education committee. Révész did not secure a mandate in the 2014 parliamentary election, however he became a Member of Parliament again in September 2014, when he replaced Róbert Rácz.
