Muravchik was one of the group of writers who moved away from the political left in the 1960s and 1970s and came to be called "neoconservatives." In 1986, a ''Wall Street Journal'' editor wrote: "Joshua Muravchik may be the most cogent and careful of the neoconservative writers on foreign policy." Muravchik wrote in defense of neoconservative position when it became highly controversial during the years of George W. Bush’s presidency.
Muravchik received an undergraduate degree from City College of New York (1970) and a Ph.D in international relations from Georgetown University (1984). He also received an honorary doctorate from the Aurel Vlaicu University of Romania (2004). In 1998, he received a citation from the Polish parliament for his activities on behalf of Solidarity.
Muravchik was National Chairman of the Young People's Socialist League (YPSL) from 1968 to 1973, and executive director of the Coalition for a Democratic Majority from 1977 to 1979. He was also an aide to the late Congressman James G. O'Hara (D-Mich.) in 1975 and to the late Senator Daniel Patrick Moynihan (D-NY) in 1977 and as a campaign aide to the late Senator Henry M. Jackson in his pursuit of the 1976 Democratic presidential nomination.
Muravchik serves on the board of trustees and the executive committee of Freedom House. In 1995, he became a founding member of the Foundation for Democracy in Iran, a non-profit organization established with grants from the National Endowment for Democracy. In 2006, Muvarchik had an opinion piece published in the Los Angeles Times entitled "Bomb Iran". In it, he argues that the prospect of Iranians overthrowing their government seemed "even more remote today than it did a decade ago", compared the Iranian government to the Bolsheviks and the Nazis, and claimed that Iran was harboring Al Qaeda.
Muravchik argued in ''The Washington Post'' that the United States should attack Iran, stating: "Does this mean that our only option is war? Yes, although an air campaign targeting Iran's nuclear infrastructure would entail less need for boots on the ground than the war Obama is waging against the Islamic State, which poses far smaller a threat than Iran does."