Here are some key questions about what it all means.
- What has Jeremy Corbyn said about a second referendum?
The Labour leader has said he would put forward or support an amendment in favour of a public vote to stop Theresa May's deal being "forced on the country" - if the party's own Brexit demands are not met.
He will first seek to enshrine the party's five Brexit demands in law by tabling an amendment to the Government's motion this week.
If the plan is rejected, Labour will then support a second referendum.
- Is this a shift in Labour policy?
Labour has previously distanced itself from backing a second referendum, and its general election manifesto in 2017 accepted the result of the 2016 vote.
Former Labour frontbencher Owen Smith was sacked last year over his support for a second referendum.
But Mr Corbyn has come under pressure from pro-EU MPs to throw the party's weight behind a second referendum, and at the Labour Party conference in September, party delegates voted to keep the option of a second vote on the table.
Some say the Labour leader's latest move is an attempt to stop further defections following last week's Labour split.
- What was the reaction to the move?
The announcement was met with divided opinion among Labour's own MPs.
Shadow foreign secretary Emily Thornberry told the BBC a second referendum would "break the logjam", while David Lammy, a supporter of the People's Vote campaign for a second referendum, said a public vote would bring a "decisive mandate to move forward".
But Caroline Flint, Labour MP for Don Valley, said the party was in danger of overturning the election promise to respect the 2016 referendum result.
"We can't ignore millions of Labour Leave voters," she tweeted. "There are Labour MPs like me who will not support a second ref."
And Lucy Powell said she "remained to be convinced" on supporting a second referendum, predicting around 25 of her colleagues would not vote for it.
Chuka Umunna, one of the eight MPs who quit the party to join the Independent Group, said the announcement was "better late than never".
- What would Labour want to be on the ballot paper if there was a second referendum?
It is not clear what the proposed referendum would be on, but a Labour source heavily hinted that a remain option would be on the ballot paper in a second vote, saying: "We've said in the past that if there were another referendum that remain would need to be on the ballot paper."
A briefing paper reportedly given to Labour MPs said any referendum would need to have "a credible Leave option and Remain".