The US Secretary of State, Condoleezza Rice, has defended the US against allegations that it ran a network of "ghost flights" and secret prisons around the world where terror suspects could be interrogated with little concern for international law.
The BBC News website profiles some of the detainees who say they were victims of the US' secret "extraordinary rendition" policy.
The case of Khaled al-Masri, 41, a German citizen allegedly handed over to the US by Macedonian agents in 2004, helped spark controversy over so-called "ghost flights" and secret "torture prisons".
Kuwaiti-born Mr Masri was seized close to the Macedonian border as he headed towards Albania following what he has described as a row with his wife in Germany. After being held for three weeks in the Macedonian capital, Skopje, Mr Masri says he was beaten, handcuffed, blindfolded, drugged, and flown to a CIA prison in Afghanistan.
Mr Masri alleges he was held in Afghanistan for five months, often in solitary confinement, while US agents interrogated him. He says he was beaten frequently, and told he was being held in "a country without laws".
Eventually, the Washington Post has reported, the CIA concluded they had simply made a mistake, and Mr Masri was returned to the Balkans, dumped close to where he was found, and eventually made his way back to Germany.
German Chancellor Angela Merkel has announced that his case will be investigated by a German parliamentary committee.
Syrian-born Maher Arar, 34, was picked up by US immigration in September 2002 as he passed through New York's JFK airport. He was heading home to Canada after a family holiday in Tunisia. After days of questioning, he says he was placed on a private jet, shackled, bound, and flown to Syria.
Mr Arar has told the BBC that he was repeatedly tortured during 10 months' detention in Syria - often whipped on the palms of his hands with metal cables - before being released after intervention by the Canadian government.
In 2004 Mr Arar filed a lawsuit against senior US officials, claiming that whoever sent him to Syria knew he would be tortured by intelligence agents.
Mamdouh Habib, an Egyptian-born Australian citizen, was arrested in Pakistan in October 2001.
At the end of the year, after interrogation in Pakistan, where he was thinking of settling with his family, Mr Habib was flown to Egypt.
He told the BBC that he did not know who had held him, but had seen Americans, Australians, Pakistanis, and Egyptians among his captors.
He said he had been beaten, given electric shock and brainwashed.
After signing confessions of involvement with al-Qaeda, which he has now retracted, Mr Habib was transferred to the US detention centre in Guantanamo Bay. He was released without charge in January 2005.
Binyam Mohammed, an Ethiopian national, is one of just a handful of "enemy combatants" held by the US at Guantanamo Bay to have been charged with terrorism offences.
He is thought to have travelled to Afghanistan in June 2001, and was seized in Pakistan in April 2002, accused of terrorism and eventually transferred to Guantanamo Bay.
Before arriving at the US base, though, Mr Mohammed alleges incarceration and torture in so-called "ghost prisons" in Morocco and Afghanistan. Extracts from his diary, carried in The Guardian, a UK newspaper, describe how interrogators repeatedly used a scalpel to lacerate his chest and genitals.
He also alleges that he was bombarded with questions about senior al-Qaeda leaders subsequently captured by the US, and deprived of sleep by having heavy rock music played loudly throughout the day and night.
He was eventually transferred to Guantanamo Bay and charged on 7 November 2005.