Muslim men in India are allowed to divorce through "triple talaq" – a custom that involves saying the word talaq three times in succession. The divorce is instant and unilateral.
Given the sensitivity of the subject - the right to practise one's religion vs a woman's human rights as guaranteed under the Indian constitution - the five Supreme Court judges have been chosen carefully. Each one comes from a different faith: a Muslim, Hindu, Christian, Parsi and Sikh.
The hearing began on Thursday in response to several petitions filed by Muslim women challenging the practice. Instead of ruling on each individual petition, the Supreme Court decided to rule on the intrinsic legality of triple talaq.
No one knows how many Muslim men use triple talaq – it is very far from being the norm – but stories have increasingly appeared in recent years of women whose lives have been destroyed by this arbitrary and cruel way of ending a marriage.
The Bharatiya Muslim Mahila Andolan, a Muslim women's rights group which started the campaign to abolish the practice, said in 2015 that more than three quarters of the women who contacted it for help had been divorced in this way.
"It is a totally un-Koranic practice. It is an expression of patriarchy, not religion,'" said Noor Jehan, co-convener of the Andolan. "It is sanctioned not by scripture but by custom, and customs can be reformed."
A government committee set up in 2013 to look into women's status published a report in 2015 recommending a ban. It said the custom "makes wives extremely vulnerable and insecure regarding their marital status".
By March, more than a million Muslims from across India had signed a petition supporting a ban.
But an influential organisation, the All India Muslim Personal Law Board, opposes the abolition of the instant divorce. In its petition to the Supreme Court, the Board argues that if Muslim men are denied triple talaq, they might murder their wives to get rid of them.
Implying that triple talaq was good for women, the Board said that if a man had to face the hassle of time-consuming and expensive legal proceedings to divorce his wife, "he may resort to illegal, criminal ways of murdering or burning her alive".
However, as the debate has intensified, some Muslim religious figures have come out in support of a ban, saying triple talaq is an aberration and it is time for the Muslim community itself to start reform by issuing divorce guidelines that protect women's rights.