What next for Theresa May after seeing off bid to replace her as Tory leader?

Theresa May lives to fight another day after dramatically defeating a bid to oust her as Tory leader.

But with major Brexit difficulties still unresolved and European leaders seemingly unable to offer the fundamental reforms demanded by Mrs May's critics, is the Prime Minister safe or has she merely bought herself time?

Here are the challenges still facing Mrs May in the weeks to come:

– Back to Brussels

After a whistlestop tour of European capitals on Tuesday, Mrs May returns to Brussels on Thursday for a summit of EU leaders.

The political crisis in the UK has forced Brexit on to the agenda for the summit, which was already in the diaries of the continent's leaders.

In his invitation letter to leaders of the EU member states, European Council president Donald Tusk said "given the seriousness of the situation", Brexit would be discussed, with the heads of the 27 remaining states expected to hear from Mrs May and adopt conclusions on the next steps.

He has insisted that the EU "wants to help" Mrs May but "the question is how".

The Prime Minister wants further concessions about the "backstop" – the contingency measures designed to prevent a hard border with Ireland even if trade talks break down.

She has suggested the Government is looking at how to give "democratic legitimacy" to the backstop through giving MPs a vote on it and enabling the Commons to force the Government to ensure it cannot be in place "indefinitely".

European Commission president Jean-Claude Juncker has stressed that the Withdrawal Agreement will not be renegotiated, but "further clarifications" are possible – measures which are unlikely to go far enough to win over Tory Eurosceptics.

– Finally facing the Commons

The decision to postpone a vote on the Withdrawal Agreement and Political Declaration, which was due to go ahead on Tuesday, was instrumental in persuading Tory critics to trigger the confidence motion.

The Prime Minister cannot avoid facing the Commons indefinitely if she wants an agreement in place by the UK's departure date from the European Union on March 29 2019.

Mrs May has promised to bring the deal, with any late tweaks she can secure in Brussels, back to MPs by January 21.

Unless major reforms are secured, it appears highly likely that the coalition of Tory rebels and opposition parties opposed to the Brexit plan will have enough support to defeat the Government.

– A Commons motion of no confidence in the Government

Labour did not table a motion of no confidence after Mrs May pulled the Commons vote on her Brexit deal, preferring to wait on the sidelines while Tory MPs fought among themselves.

But other opposition parties at Westminster – the SNP, Liberal Democrats, Plaid Cymru and the Green Party – have called on Jeremy Corbyn to table a confidence motion "before it is too late" for Parliament to take control of the Brexit process.

A defeat when the deal is finally put to the test in the Commons could be the event which prompts Mr Corbyn to strike.

The Democratic Unionist Party, whose 10 MPs the Tories rely on for a majority, have promised to support the Government in a confidence motion if Mrs May's Brexit plan is scrapped or defeated.

But their support is not tied to Mrs May personally and they would not back her if she sought to press ahead with her deal.

If a majority of MPs back a motion of no confidence, it would start a countdown which could lead to an early election.

Unless a government can win a confidence vote within 14 days, there would be another general election.