Extradition is the official process by which one nation or state requests and obtains from another nation or state the surrender of a suspected or convicted criminal. Between nation states, extradition is regulated by treaties. Among sub-national regions (for example, the individual states of the U.S.), where extradition is required by law it is more accurately known as rendition.
The consensus in international law is that a state does not have any obligation to surrender an alleged criminal to a foreign state as one principle of sovereignty is that every state has legal authority over the people within its borders. Such absence of international obligation and the desire of the right to demand such criminals of other countries have caused a web of extradition treaties or agreements to evolve; most countries in the world have signed bilateral extradition treaties with most other countries. No country in the world has an extradition treaty with all other countries; for example, the United States lacks extradition treaties with over fifty nations, including the People's Republic of China, Namibia, and North Korea.
The refusal of a country to extradite suspects or criminals to another may lead to international relations being strained. Often, the country to which extradition is refused will accuse the other country of refusing extradition for political reasons (regardless of whether this is justified), as in the case of Ira Einhorn where some US commentators pressed President Jacques Chirac of France, who does not intervene in legal cases, to permit extradition when the case was held up due to differences between French and American human rights law.
The matters are often complex when the country from which suspects are to be extradited is a democratic country with a rule of law. Typically, in such countries, the final decision of extradition lies with the national executive (prime minister, president or equivalent). However, such countries typically allow extradition defendants recourse to the law, with multiple appeals. These may significantly slow down the procedures. On the one hand, this may lead to unwarranted international difficulties, as the public, politicians and journalists from the requesting country will ask their executive to put pressure on the executive of the country from which extradition is to take place, while that executive may not in fact have the authority to deport the suspect or criminal on their own. On the other hand, certain delays, or the unwillingness of the local prosecution authorities to present a good extradition case before the court on behalf of the requesting state, may possibly result from the unwillingness of the country's executive to extradite.
For example, there is at present a disagreement between the United States and the United Kingdom about the Extradition Act 2003 (text here) that dispenses with the need for a prima facie case for extradition.
It is important to emphasise, however, that even had the treaty been ratified by the U.S., the treaty would still be one-sided, because it stipulates that extradition requests from the UK to the U.S. must show a "reasonable case" that the suspect committed the offense, but requests from the U.S. to the UK have no such requirement imposed on them.
This came to a head over the extradition of the Natwest Three from the UK to the U.S., for their alleged role in the Enron fraud, with various British political leaders weighing in to attack the British government's handling of the issue  . The former leader of the UK's Liberal Democrat party, Sir Menzies Campbell, had argued that the U.S. had not ratified the treaty primarily due to the influence of what he calls the "Irish lobby" - which, he said, is opposed to the treaty because it could make it easier for Britain to have alleged IRA terrorist suspects extradited from the U.S.
The precedent of the Natwest Three may also be used to extradite/prosecute Philip Watts in connection with the Royal Dutch Shell reserves scandal. The press has carried vocal criticisms of the present extradition arrangements from the UK's business community, some of whom stated that they were avoiding doing business with or in the U.S., because of legal concerns such as the extradition treaty, among other concerns. 
Issues of international law relating to extradition have proven controversial in cases where a state has abducted and removed an individual from the territory of another state without previously requesting permission, or following normal extradition procedures. Such abductions are usually in violation of the domestic law of the country in which they occur, as infringements of laws forbidding kidnapping. Many also regard abduction as violation of international law - in particular of a prohibition on arbitrary detention. A small number of countries have been reported to use kidnapping to circumvent the formal extradition process.
Notable or controversial cases involving abduction of foreign citizens:
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See main article: Extraordinary rendition. "Extraordinary rendition" is an extra-judicial procedure and policy of the United States in which criminal suspects, generally suspected terrorists or supporters of terrorist organisations, are sent to countries for imprisonment and interrogation. The procedure differs from extradition as the purpose of the rendition is to extract information from suspects, while extradition is used to return fugitives so that they can stand trial or fulfill their sentence. Critics of the procedure have accused the CIA of rendering suspects to other countries in order to circumvent U.S. laws prescribing due process and prohibiting torture.