The 33-year-old is accused of involvement in the death of his 28-year-old wife, Anni, who was shot as the couple travelled in a taxi in Cape Town back in November 2010.
Hugo Keith QC, representing the South African government, began proceedings for the five-day hearing at Westminster Magistrates' Court today by summarising the history of the case as Anni Dewani family watched from the public gallery.
Shrien was excused from attending the hearing but his father Prakash and brother Preyen were present in the court.
They have previously claimed that he would be a high suicide risk if extradited, and his human rights may be violated due to the risk of being violently attacked.
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South African authorities have offered assurances that Shrien would be kept in a single cell if he returns, and therefore would be at less risk of attack.
In April, prosecutors said his condition had improved "significantly", but in May, the court was told he had suffered a relapse.
Anni Dewani was shot when a taxi in which the couple were travelling was hijacked in Gugulethu.
Shrien and driver, Zola Tongo, were ejected from the car before Anni was driven away and killed.
She was found dead in the back of the abandoned vehicle with a bullet wound to her neck.
In 2012, Xolile Mngeni was convicted of premeditated murder for shooting her.
Prosecutors claimed that Mngeni was a hitman hired by Shrien to kill his wife, something that he has consistently denied.
Another accomplice, Mziwamadoda Qwabe, also pleaded guilty to charges over the murder and was handed a 25-year prison sentence.
Both Tongo and Qwabe have claimed Shrien was involved in planning the murder.