Universal jurisdiction is a concept in international law, in which certain offenses are considered sufficiently grave that any Requesting State (i.e., nation) may apprehend, or ask for extradition of, an individual who has been charged, by a second state. In the most general form, there is no requirement that the defendant be a national of the Requesting State, that the the victim(s) be a citizen of the Requesting State, or, indeed, that there are any links to the Requesting State.  In principle, it overcomes collunsion, by national governments, 
Some of its legal framework relates to the legal doctrine of hostis humani generis, most commonly applied to pirates or slavers, who could be taken into custody by any navy. While the International Military Tribunal (Nuremberg) was not established by treaty, and indeed prosecuted and executed defendants based on ex post facto rules of criminality, it is treated with a good deal of legitimacy if not universally accepted precedent. The International Military Tribunal (Tokyo) had more legitimacy, because it operated under the a provision of the Japanese surrender, in which the Japanese government, "(which, at least formally, retained sovereign power in Japan after the war) acceded, in the Instrument of Surrender to prosecution of Japanese nationals before the International Military Tribunal for the Far East."
The Geneva Conventions call for prosecution of offenders by any concerned state, but do not establish a structure for trying individuals.
More contemporary usage ties to the Rome Statute establishing the International Criminal Court (not to be confused with the International Court of Justice; not all nations, including a number of major ones, have ratified the ICC treaty.
Article 12 of the Rome Statute, is considered to supplement jurisdiction based on Security Council action under Chapter VII of the United Nations Charter or consent by the defendant’s state of nationality. "If a crime is committed by a non-party national on that non-party’s territory, then the ICC may not exercise jurisdiction."  It applies when the conduct in question
- took place in the territory of a signatory state or a vessel or aircraft of its registry
- was by a citizen of a signatory state
- consents to ICC jurisdiction for that case
That territorial basis would empower the court to exercise jurisdiction even in The Rome Statute specifies a "State Party which has received a request for provisional arrest or for arrest and surrender shall immediately take steps to arrest the person in question in accordance with its laws and the provisions of [the Rome Statute]. 
In the 1984 case of Filartiga v. Pena-Irala, the U.S. Second Circuit Court of Appeals, held that torturers fell under universal jurisdiction, and, further, that the doctrine of command responsibility applied to the superiors of persons actually committing torture. In the 1987 case of Forti v. Suarez Mason, the US Circuit Court for the Northern District of California held that torturers fell under universal jurisdiction.
The United States has not ratified the Rome Statute and is not an ICC participant.
Perhaps the best-known recent case dealt with the 1998 Spanish request that the United Kingdom apprehend Augusto Pinochet for offenses committed in Chile. This was based on Spain's 1985 Organic Law that defined the jurisdiction of Spanish courts over the obvious case when the criminal act took place on Spanish soil, the less obvious case when alleged crime was committed by a Spaniard outside Spain, or when the crime is of international concern, such as genocide, piracy and terrorism. 
Spain has been an activist country in pursuing individuals believed to have committed relevant crimes, but it is considering legislation, called the Reform of the Judiciary Act, reducing its scope to situations where the crimes must have been committed against Spaniards, or at least have some historic link to Spain. In the past, Spanish courts have considered actions related to alleged crimes in Rwanda, Tibet, Guatemala, and China. The reports also suggest that the arrests must be made in Spain; extradition will not be used.  The proposed legislation may have been triggered by a Spanish judge, Fernando Andreu, ordering an investigation into whether an Israeli actions in the Gaza Strip  constituted a crime against humanity.
Complexities of the Middle East
George Fletcher, professor of jurisprudence at the Columbia University law school, strongly opposes the concept of universal jurisdiction.  In the case of Belgium's actions against Prime Minister of Israel Ariel Sharon for alleged war crimes in the 1981 Israeli operations in Beirut, there was no direct Belgian interest. Subsequently, the International Court of Justice ruled that Sharon, while Prime Minister, had immunity to individual prosecution. The Belgian Supreme Court, however, then held other officials did not have sovereign immunity. Israel threatened to invoke universal jurisdiction over 1961 Belgian activities in the Congo.
If a case were tried in the ICC, it would be a different procedure than a national court asserting universal jurisdiction. Fletcher also opposes ICC jurisdiction regarding the 2009 Gaza conflict. He brings up the point that the Rome Statute of the ICC assumes good-faith investigation by nations, as opposed to non-state actors such as the Palestinian Authority or Hamas. From this, he argues that it would be double jeopardy for an external tribunal to try individuals cleared of wrongdoing by their own national investigation. John Dugard, a South African law professor who headed the Arab League fact-finding mission, argues the opposite position. 
- Universal Jurisdiction: Questions and answers, Amnesty International
- Madeline Morris (2000-2001), Universal Jurisdiction in a Divided World: Opening Remarks, "Universal Jurisdiction: Myths, Realities and Prospects", New England Law Review 35: 337-361, p. 337
- Madeline Morris (Winter 2001), High crimes and Misconceptions: the ICC and Non-Party States, (adapted from) International Crimes, Peace and Human Rights, edited by Dinah Shelton, 2000, p. 34
- Rome Statute of the International Criminal Court, International Criminal Court, 1 July 2002
- Morris 2001b, p. 1-2
- ICC Rome Statute, Article 59, p. 40
- The Spanish National Court: An Overview, Center for Justice and Accountability
- Devin Montgomery (February 01, 2009), Reports confirm Spain considering limits on universal jurisdiction
- John Kifner (July 24, 2002), "Gaza Mourns Bombing Victims; Israel Hastens to Explain", New York Times
- George P. Fletcher (4 March 2003), "Should One Nation Be Able to Judge the Entire World? Belgium's Prosecution of Ariel Sharon, and Other Invocations of "Universal Jurisdiction"", Findlaw
- George Fletcher (23 July 2009), "Don't Go There", New York Times
- John Dugard (23 July 2009), "Take the Case", New York Times