Events over the next two days will have a major impact on how, when - and if - the UK leaves the European Union.
- What is happening in Westminster?
MPs will vote on Wednesday on whether they want to leave the European Union without a Withdrawal Agreement and Political Declaration - a no-deal Brexit.
The Prime Minister warned that a no-deal scenario would be "bleak", with a "significant economic shock", the loss of security co-operation with Europe and the prospect of the break-up of the UK as support for Scottish independence and a united Ireland could increase.
Should MPs reject that, there will be another vote on whether Parliament wants to seek ?an extension to Article 50 - delaying the UK's departure beyond the current March 29 deadline.
But Mrs May stressed that would not resolve the divisions in the Commons and could instead hand Brussels the power to set conditions on the kind of Brexit on offer "or even moving to a second referendum".
Second Commons humiliation for Theresa May as she loses Meaningful Vote by 149 votes- How could Brexit be delayed and for how long?
To secure an extension to Article 50, Mrs May would need the support of the 27 other EU states. They are likely to agree to an extension as long as there was a prospect of a deal being reached - or a referendum or general election which could change the political landscape at Westminster.
European Commission president Jean-Claude Juncker said that Brexit should be completed before the European elections which take place between May 23 and 26.
"If the UK has not left the EU by then, it will be legally required to hold these elections," he said.
If a longer extension was sought, that would mean taking part in the elections, something likely to fuel Eurosceptic anger - and potentially see Nigel Farage standing for the new Brexit Party.
- Will the Prime Minister seek further changes in Brussels?
Mr Juncker was clear during his meeting with the Prime Minister in Strasbourg that there was no more room for movement.
"In politics, sometimes you get a second chance. It is what we do with this second chance that counts. Because there will be no third chance," he said.
"There will be no further interpretations of the interpretations; and no further assurances of the re-assurances."
But a European Council summit on March 21 could give Mrs May one last chance to persuade her fellow leaders face-to-face that she needs extra help to get a deal over the line.
- So what happens on March 29?
Impossible to say at this stage. If a deal is somehow reached and legislated for then although the UK will formally leave the EU at 11pm, very little will change as a transition period will smooth progress to the UK's new future.
If there is a delay, the UK will still be in the European Union until the extension period expires.
But if there is a no-deal Brexit, things are a lot more uncertain - the Government has been ramping up preparations to try to prevent shortages of food and medicine amid fears that increased bureaucracy will clog up key ports where goods arrive from the Continent.