Neoconservatism is a political philosophy and ideology that combines many traditional conservative opinions with an emphasis on the importance of foreign policy and using American power to push democracy forward. This originated in a number of places - strongly anticommunist liberals, strong support for Israel, dissent from the left. The University of Chicago philosopher Leo Strauss is seen as one of the foundational figures in pushing forward neoconservatism - believing in noble lies (religion being a prime example for Strauss), the telling of which can convince people to act morally.
Another view of its foundation came from conservative thinker Murray Rothbard, who saw it as the successor to Frank S. Meyer's fusionism. Having rejected Communism, Rothbard saw Meyer as favoring U.S. strong U.S. militarism, and uncritically embracing anyone who opposed the Soviets and Communism. In Rothbard's view, this allowed Truman-Humphrey social democrats to enter the conservative movement, and, after Meyer's death, eventually replace fusionism with neoconservatism.
Neoconservatives often advocate military intervention, and drove the decision to start the Iraq War. Influential neoconservatives, through the Project for the New American Century, advocated Iraqi regime change beginning with an open letter in 1998.
As mentioned, they also looked to past political philosophy. Strauss emigrated to the U.S. from Germany, where he had written on Thomas Hobbes: "Hobbes's political philosophy is the first peculiarly modern attempt to give a coherent and exhaustive attempt to the question of man's right life, which is at the same time the right order of society." 
Right. And I think that’s a fair description, and I suppose all of us were liberal at one time. I was liberal in high school and a little bit into college. But reality and rigor are important tonics, and if you got into the world of international affairs and you looked with some rigor at what was going on in the world, it was really hard to be liberal and naïve...Anyone who looked at the facts in Nineteen Thirty-six knew what was coming or could at least see that the balance of power was in the process of shifting from one in which the democracies could expect to contain this growing totalitarian threat in Nazi Germany to a balance in which they couldn’t...the indulgence of Saddam led to the invasion of Kuwait.
Neoconservatism had become especially influential in the United States of America following the 9/11 attack. To an extent, it reapplied Cold War doctrine to radical Islamism, also keeping a strong relationship with the State of Israel. Their greatest disciples in the Bush Administration included the secretary of Defense, Donald Rumsfeld, the Vice President Dick Cheney and Paul Wolfowitz who were all at one time or another members of the neoconservative Project for the New American Century think-tank. Their influence waned somewhat as the Iraq War dragged on; Rumsfeld and Wolfowitz were replaced in the Bush Administration.
Neoconservative views are not visible in the Obama Administration. Nevertheless, they are seen as "New Right" as opposed to paleoconservatism and libertarianism in the restructuring of the U.S. political right.
Newsweek quoted Vin Weber, in January 2010, as describing neoconservatism as "the dominant intellectual force on foreign-policy thinking in the Republican Party," as opposed to realism and paleoconservatism. The article called William Kristol the most influential neoconservative.
A number of organizations, with all- or significantly-neoconservative identified leadership, have been forming for the 2010 elections or in opposition to the Obama Administration. Many of the same people are involved in these formations, such as William Kristol on the boards of Keep America Safe and the Emergency Committee for Israel, and Foreign Policy Initiative.
There are several groups of relatives in neoconservative leadership. William Kristol is the son of Irving Kristol. Liz Cheney is the daughter of Dick Cheney. Robert Kagan is the son of Donald Kagan and brother of Frederick Kagan; Frederick Kagan is married to Kimberly Kagan. Rachel Abrams is the spouse of Elliott Abrams and daughter of Midge Decter and Norman Podhoretz.
- Llewellyn H. Rockwell, Jr., ed., Frank Meyer and Sydney Hook, Essays of Murray N. Rothbard
- George Packer (2005), The Assassins' Gate, Farrar, Straus and Giroux, ISBN 0374299633, pp. 53-54
- Leo Strauss (1936), The Political Philosophy of Hobbes: Its Basis and its Genesis, University of Chicago Press, p. 1
- Ben Wattenberg (14 November 2002), "Richard Perle: the Making of a Neoconservative", PBS
- Francis Fukuyama (2006), America at the Crossroads: Democracy, Power, and the Neoconservative Legacy, Yale University Press, ISBN 0300113994
- David Margolick (22 January 2010), "The Return of the Neocons", Newsweek