The key issues included:
The fairness of the Extradition Act 2003 (covering the US) and the European Arrest Warrant.
Whether the country asking for someone to be extradited should provide evidence to be tested first in the British courts.
Whether the UK should bar extraditions where offences have been largely committed in the UK.
Here are some of the recent cases that have raised questions about extradition:
GARY McKINNON: THE HEALTH ISSUE
Gary McKinnon has been fighting extradition to the US for several years
The home secretary is currently reviewing the case of Gary McKinnon, whom the US authorities want to extradite for alleged hacking of US military computer systems.
Glasgow-born Mr McKinnon, who has Asperger’s syndrome, faces up to 60 years in jail for hacking into Pentagon and Nasa computers between February 2001 and March 2002.
The 45-year-old, who lives in north London, does not deny hacking into the systems but insists he was seeking evidence of UFOs.
The US decided to indict Mr McKinnon after he was arrested in 2002, although extradition proceedings did not begin until 2005.
He has since appealed unsuccessfully to the House of Lords and the European Court of Human Rights to avoid extradition.
His lawyers also lost an appeal for him to be prosecuted in the UK on lesser charges, with the Crown Prosecution Service saying the US was the best place for the case to be heard.
Now campaigners say such a vulnerable person should not face trial in the US, for medical reasons.
There has been a long-running campaign for Mr McKinnon to be allowed to remain in the UK, and many politicians, including Deputy Prime Minister Nick Clegg, have expressed concerns about the case.
Mr McKinnon’s mother, Janis Sharp, is also fighting to keep her son in the country.
It is not yet known when Theresa May will decide whether Mr McKinnon must be extradited.
In May, while on a UK state visit, Mr Obama said he would “respect” the British legal process.
BABAR AHMAD: ACCUSED OF OFFENCES IN UK
Babar Ahmad, an IT worker from Tooting in south London, has been held in jail for more than seven years while contesting extradition to the United States.
His family says that if he had committed crimes he should be tried in the UK. Their campaign to have him tried in a British court has become one of the top 10 e-petitions on the official government website.
US investigators accuse Mr Ahmad, who denies wrongdoing, of running online fundraising operations for jihadists in Chechnya and Afghanistan. He was arrested for extradition in 2004 – but only after Scotland Yard had arrested and released him without charge months earlier.
Parliament’s Joint Committee on Human Rights has called for the US-UK treaty to be renegotiated to prevent people like Mr Ahmad being extradited if the British authorities have already decided not to prosecute someone for an offence based on the same evidence.
A key link between Mr Ahmad and the US is that one of the alleged websites was based in Connecticut. Parliament has passed a law, known as the “forum bar”, which could be invoked to prevent people being tried abroad for offences which should be prosecuted in the UK. The measure has never been brought into force.
Mr Ahmad is now waiting for a final decision on his case at the European Court of Human Rights.
ANDREW SYMEOU: QUALITY OF EVIDENCE
Andrew Symeou was cleared two years after he was extradited to Greece in July 2009 to face manslaughter charges in connection with the death of Jonathan Hiles at a nightclub on the Greek island of Zakynthos.
Mr Hiles, 18, from Cardiff, who was on holiday in July 2007 when he fell from a dance podium, died from a brain injury.
Mr Symeou, 22, from Enfield, north London, was accused of punching the teenager in the face, knocking him out in the process and causing him to fall from the podium.
He had denied being in the nightclub at the time.
In 2009, Mr Symeou was extradited to Greece under the European Arrest Warrant.
He spent 10 months in a Greek prison and became the subject of a campaign to free him by the charity Fair Trials International, with the charity saying much of the apparent evidence against him was based on details obtained by Greek police officers who intimidated witnesses.
On 17 June 2011, the jury found Mr Symeou not guilty. Mr Hiles’ father, Denzil, has said he will appeal against the decision.
MIKOLAJ KOWALSKI: PROPORTIONALITY
According to Fair Trials International, Mikolaj Kowalski – not his real name – a Polish schoolteacher and grandfather who lives in Bristol, was sought on an European Arrest Warrant in 2010 to face trial for “theft” in Poland in 2000.
The charity said the alleged offence referred to a period when Mr Kowalski withdrew money from his bank taking him over the agreed overdraft limit, but the entire debt was repaid to the bank after it repossessed and sold his home.
In 2004, Mr Kowalski moved with his family to the UK.
But on 23 July 2010, Fair Trials International said he was arrested by British police and threatened with a criminal trial for a debt he paid off many years ago.
It said Mr Kowalski, who has numerous health problems, was very worried about being sent to prison in Poland and being separated from his family, including his wife who cares for him.
In April 2011 the English court decided Mr Kowalski’s extradition should not go ahead due to his health problems, but the EAW remains in place and he is unable to leave the UK.