text: Ex-Libyan dissident Abdul Hakim Belhaj says MI6 helped to arrange his and his wife's rendition - saying they were covertly taken from Thailand to Libya.
  The case, involving allegations against ex-Foreign Secretary Jack Straw and an ex-MI6 chief, prompted an unprecedented battle over whether it can even begin.
  The Supreme Court is to decide whether the couple can sue the UK government.
  Police have investigated the claims but the Crown Prosecution Service is yet to announce its charging decision.
  The so-called extraordinary rendition programme operated for years in the wake of the 9/11 attacks of the US.
  The claims involve the secret detention and transfer of terror suspects between countries for interrogation, allegedly including torture.
  The UK and rendition allegations
  Government can be sued over rendition claims
  Belhaj torture case against UK rejected
  Mr Belhaj, a former Islamist fighter who opposed the Libyan dictator Colonel Muammar Gaddafi, says he was seized by US forces alongside his wife, Fatima Boudchar, in 2004 as they tried to fly from Asia to the UK to seek asylum.
  The couple were taken from Thailand to Libya - and they were immediately imprisoned.
  Mrs Boudchar, then pregnant, says she was abused in prison and feared she would lose her baby before she was released three months later.
  Mr Belhaj has told British courts he was beaten, subjected to other abuses and, separately, interviewed by British intelligence officers.
  The regime sentenced him to death, but he was eventually released in March 2010.
  During the later fall of Gaddafi, papers uncovered in Tripoli revealed MI6's former head of counter-terrorism Sir Mark Allen had sent his congratulations to the Libyan regime for the "safe arrival" of Mr Belhaj.
  "This was the least we could do for you and for Libya to demonstrate the remarkable relationship we have built up over recent years," he is said to have written. "The intelligence about [Mr. Belhaj] was British."
  The couple launched a damages claim against the government, Sir Mark and former Foreign Secretary Jack Straw four years ago and have offered to settle for Â£1 and an apology.
  A High Court judge initially ruled out the claim, saying it could damage foreign relationships - but the Court of Appeal said the "grave" allegations must be examined.
  The Supreme Court must now decide whether to allow the government's final appeal which is focused on a complex legal principle.
  Ministers say the case should not proceed because it would breach a long-standing legal doctrine that prevents one state's courts from ruling on whether a foreign government acted unlawfully.
  The Court of Appeal ruled that while that principle was valid, it could not stop a British court from examining whether British agencies, officials or ministers were separately culpable.
  The four-day Supreme Court hearing is being heard before seven justices - a sign of how important they regard the issues.
  They are also looking at a similar case involving a Pakistan man, Yunus Rahmatullah, who says he was tortured by US forces after being handed over to them in Iraq by British forces.
target: One of the most controversial claims of rendition involving the UK is being heard by the Supreme Court.