Here are 10 developments in the story:
The five-judge bench will decide whether to admit a curative petition against the Supreme Court's verdict in December 2013 restoring the ban on gay sex.
"Does anyone actually oppose it?" Chief Justice TS Thakur remarked on the clutch of petitions against the ban, drawing laughter in the courtroom.
Representing a petitioner, Congress leader and senior lawyer Kapil Sibal said: "The situation at present binds the present and future generation to stigma and prejudice."
The curative petition is the last legal resort and is usually heard by judges in chambers but today's hearing took place in open court. The Supreme Court had rejected a review petition in 2014.
Gay rights activists, the NGO Naz Foundation and others including filmmaker Shyam Benegal have challenged the ruling in which the Supreme Court upheld the validity of Section 377 of the law, which makes gay sex a crime for which the punishment can be a life term. Their petition has been opposed by the Muslim personal law board and the Church of India.
On learning that the top court had kept the legal battle alive instead of throwing out the petition, activists sang: "We shall overcome."
In 2009, the Delhi High Court exempted gay sex between consenting adults from Section 377, the 1860 law which bans "carnal intercourse against the order of nature with any man, woman or animal."
The Supreme Court reversed the landmark ruling in 2013, ending four years of decriminalisation that had helped bring homosexuality into the open in largely conservative India. The court said only Parliament can remove or change laws.
The Congress appealed against the Supreme Court decision and had pledged to remove the law if it came to power, but it lost in 2014. Finance Minister Arun Jaitley has backed calls for ending the ban, though his BJP has been more cautious. "When millions of people world over are having alternative sexual preferences, it is too late in the day to propound a view that they should be jailed," Mr Jaitley said at an event last year.
In December, Congress parliamentarian Shashi Tharoor failed to introduce his bill to amend the law, with 74 members in the Lok Sabha voting against the bill and only 21 backing it, making even a debate impossible.
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