Nine Law Lords are hearing a challenge in the House of Lords over the government's right to detain terror suspects without trial or sentence.
Lord Bingham will lead the panel of nine Law Lords
The panel will weigh up the arguments of the detainees and human rights groups against those of the government.
The House of Lords - which has 12 full-time Law Lords, or senior judges - is the final court of appeal in the UK.
Nine Law Lords, rather than the usual five, are sitting because of the constitutional importance of the legal challenge.
LORD BINGHAM OF CORNHILL
As senior Law Lord, Lord Bingham will lead the panel considering the legality of the government's Anti-Terrorism, Crime and Security Act 2001 (ATCSA).
A former Lord Chief Justice, the 70-year-old is seen as a reformer who has backed the creation of a supreme court to replace the Law Lords as the country's highest court.
Made a life peer in 1996, Lord Bingham was last year beaten to the post of Oxford University chancellor by Chris Patten.
The inclusion of Lord Hoffmann on the panel may raise some eyebrows.
His failure to declare his own and his wife's links to the human rights group Amnesty International led the House of Lords to set aside its original ruling on whether former Chilean leader General Augusto Pinochet could face extradition.
He was criticised for making an "error of judgement" by the then lord chancellor, Lord Irvine.
Lord Hoffmann was criticised for failing to declare links to Amnesty
Amnesty International is also involved in the challenge before the Law Lords over anti-terror laws.
But Lord Hoffmann resigned as a director of Amnesty International Charity Ltd in September 2000 and his wife no longer works there, an Amnesty spokesman said.
Although Lord Hoffmann has gained a reputation as a liberal, he has displayed conservative tendencies in some cases.
An opera lover who has served on the board of English National Opera and on the Arts Council, he is also a keen cyclist.
LORD NICHOLLS OF BIRKENHEAD
Lord Nicholls, 71, spoke out earlier this year to criticise plans to overhaul the legal justice system.
He argued proposals to replace the law lords with a new supreme court were "misguided" and would leave senior judges in an "ivory tower".
A life peer since 1994, Lord Nicholls was in favour of allowing extradition procedures against General Pinochet to proceed.
In a landmark case brought by asbestos victims, Lord Nicholls ruled it would have been "offensive" to deny them compensation.
LORD HOPE OF CRAIGHEAD
Lord Hope was one of five Law Lords to hear supermodel Naomi Campbell's breach of privacy claim against the Daily Mirror.
He was among the majority three to rule in favour of the model, saying the paper's coverage must have seemed "a gross interference with her right to respect for her private life".
LORD SCOTT OF FOSCOTE
Lord Scott has previously clashed with the government over its failure to keep its promise to enact laws regulating the arms trade.
Lord Scott said the government must overhaul arms export laws
The author of the landmark 1996 Scott report into the arms to Iraq scandal, Lord Scott said in 2001 it was "regrettable and disappointing" that changes had not been made to legislation.
He was among five Law Lords to rule against former MI5 agent David Shayler's bid to use a "public interest" defence in his "state secrets" trial.
Lord Scott, who lists hunting among his interests, is likely to follow legislation to ban hunting with dogs closely.
LORD RODGER OF EARLSFERRY
Lord Rodger has supported attempts to counter suspected international terrorism in the past.
He was involved in a 2001 decision not to block the extradition of three men wanted in the United States on charges of conspiring with Osama bin Laden in terror attacks.
The Law Lords ruled the US should be able to extradite the men over the 1998 bombings of American embassies in Kenya and Tanzania despite the fact the attacks were not on US soil.
Lord Rodger has also been a member of the Mental Welfare Commission for Scotland and senator of the College of Justice.
LORD WALKER OF GESTINGTHORPE
Workers' rights were at the forefront for Lord Walker earlier this year.
Made a life peer in 2002, he was among four Law Lords to rule that employers must take the initiative to protect employees they know are vulnerable to stress-related illness.
Lord Walker sat on a panel of nine judges who in July decided to abolish the mandatory death penalty for murder in Jamaica.
BARONESS HALE OF RICHMOND
Baroness Hale earlier this year became the first female Law Lord to be appointed in Britain.
She was one of those to vote in favour of Miss Campbell in her privacy case against the Daily Mirror, saying people recovering from drug addiction needed dedicated and committed support.
She said: "Blundering in when matters are acknowledged to be at a fragile stage may do great harm."
In June she was one of four out of five law lords to rule that a gay couple had the same legal rights as a married couple.
Lord Carswell is one of the newest additions to the ranks of Law Lords, having been appointed in January this year.
He ruled in July, alongside Baroness Hale and Lord Rodger, that police should be allowed to build the largest DNA and fingerprint database possible.
He was Lord Chief Justice of Northern Ireland from 1997 to 2004.