Boris Johnson and Jeremy Hunt have been outlining their Brexit plans as they campaign for the votes of 160,000 Conservative Party members who will decide which of them succeeds Theresa May as prime minister and Conservative Party leader.
Boris Johnson is the UK's new prime minister and will now begin the task of trying to deliver Brexit.
They have been explaining what changes they want to make to Mrs May's Withdrawal Agreement, how they plan to deliver them before the Brexit deadline of 31 October and their views on leaving without a deal.
The former foreign secretary has pledged the UK will leave the EU on 31 October, "do or die", accepting that a no-deal Brexit will happen if an agreement cannot be reached by then.
The Withdrawal Agreement (WA) is the "divorce deal" negotiated by the UK government and the European Union (EU). As part of it, the UK agreed to pay the EU a "divorce bill" (estimated at £39 billion), guarantee EU citizens' rights and sign up to the Irish backstop - an insurance policy designed to avoid a hard border in Ireland.
He has called the withdrawal agreement "dead" but says he will "take the bits that are serviceable and get them done" - such as guaranteeing the rights of 3.2 million EU citizens in the UK.
The deal allowed for a transition period after Brexit, during which things like UK/EU trade would effectively stay the same, while both sides worked out their future relationship. But the Withdrawal Agreement was rejected three times by MPs - leading to Mrs May's downfall.
The withdrawal agreement (WA) is the deal negotiated by the UK government and the European Union (EU) to settle the basis on which the UK will leave. As part of it, the UK agreed to pay the EU a "divorce bill" (estimated to be £39bn), guarantee EU citizens' rights and sign up to the Irish backstop - an insurance policy designed to avoid a hard border in Ireland.
So what would the two candidates do differently - and what obstacles might they face?
The deal allowed for a transition period after Brexit, during which things like UK-EU trade would stay the same, while both sides worked out their future relationship. But the withdrawal agreement was rejected three times by MPs - leading to Theresa May's downfall.
Boris Johnson
The former foreign secretary has pledged that the UK will leave the EU on 31 October, "do or die". He has called the Withdrawal Agreement "dead" but says he would "take the bits that are serviceable and get them done" - such as guaranteeing the rights of 3.2 million EU citizens in the UK. He would try to get a deal by 31 October but if that wasn't possible, then the UK would leave on "WTO terms" - effectively a no-deal Brexit.
Irish border
Irish border
Mr Johnson says this should be tackled "on the other side of 31 October" during what he's calling an "implementation" period. After Brexit, Northern Ireland and the Republic of Ireland could be in different customs and regulatory regimes, which might mean products being checked at the border. To avoid border posts (which some believe could threaten the peace process), Mrs May and the EU agreed on the backstop - keeping both sides in a customs union. This proved controversial because it would stop the UK doing its own trade deals.
After Brexit, Northern Ireland and the Republic of Ireland could be in different customs and regulatory regimes, which might mean products being checked at the border. To avoid border posts (which some believe could threaten the peace process), Mrs May and the EU agreed on the backstop. In the event that no free trade deal was agreed that avoided a hard border, this insurance policy would effectively keep the UK and EU in a customs union. This proved controversial because it would stop the UK doing some of its own trade deals.
Obstacle: The President of the European Council Donald Tusk has said "the Withdrawal Agreement is not open for renegotiation". The backstop is part of the Withdrawal Agreement, which is legally binding. It is not clear what Mr Johnson means by an "implementation" period. Mrs May's deal allows for an implementation period (the EU calls it a transition period) for a number of years. But the transition period is part of the Withdrawal Agreement and Mr Johnson has declared that agreement "dead".
Mr Johnson is saying the Irish border can be dealt with after the UK leaves the EU, instead of as part of the withdrawal agreement.
Obstacle: The EU has said the Irish backstop cannot be removed from the withdrawal agreement - the deal to delay the UK's exit until the end of October specifically prohibited its renegotiation. If the UK leaves with no deal and seeks a free trade agreement, the EU has said it will not begin negotiations until the issue of the Irish border is settled.
Irish backstop
Irish backstop
Boris Johnson wants to ditch the Irish backstop - he's called it "a prison". He has said there are "abundant, abundant technical fixes" to avoid checks at the border. He concedes that there is "no single magic bullet" but points to a "wealth of solutions" instead.
Boris Johnson wants to ditch the Irish backstop - he's called it "a prison". He has said there are "abundant, abundant technical fixes" to avoid checks at the border. He concedes there is "no single magic bullet" but points to a "wealth of solutions" instead.
Obstacle: The UK and the EU have previously looked for technological solutions to the Irish border without success. The EU deputy chief negotiator, Sabine Weyand, said in January: "We looked at every border on this Earth, every border the EU has with a third country - there's simply no way you can do away with checks and controls." There are "alternative arrangements" which could help: trusted trader schemes (where businesses are certified to make sure they meet certain standards) and ways of making customs declarations away from the border, but they wouldn't eliminate the need for checks altogether. After Brexit, the EU would still require inspections of things like animal and plant products entering its Single Market, and the new entry point to that market would be at the Irish border.
Obstacle: The UK and the EU have previously looked for technological solutions to the Irish border without success. EU deputy chief negotiator Sabine Weyand said in January: "We looked at every border on this Earth, every border the EU has with a third country - there's simply no way you can do away with checks and controls." There are "alternative arrangements" which could help: trusted trader schemes (where businesses are certified to make sure they meet certain standards) and ways of making customs declarations away from the border, but they wouldn't eliminate the need for checks altogether. After Brexit, the EU would still require inspections of things like animal and plant products entering its single market, and the new entry point to that market would be at the Irish border.
£39 billion
£39bn
Boris Johnson has said he would withhold the £39 billion the UK has agreed to pay the EU and use it as a negotiating "tool" to get a better deal. Settling the UK's financial obligations (which include contributions to the EU budget and funding things like EU staff pensions) was agreed by Theresa May as part of the Withdrawal Agreement.
Boris Johnson has said he is prepared to withhold the money the UK has agreed to pay the EU and use it as a negotiating tool to get a better deal. Settling the UK's financial obligations (which include previously agreed contributions to the EU budget and funding things like EU staff pensions) was agreed by Theresa May as part of the withdrawal agreement. The figure for those obligations has been calculated at £39bn.
Obstacle: The EU has said it will not start future trade talks until the issue of money (along with citizens' rights and the Irish border) is settled. Refusing to pay would almost certainly sour relations between the two, and could lead to a legal challenge from the EU.
Obstacle: The EU has said it will not start future trade talks until the issue of money (along with citizens' rights and the Irish border) is settled. Refusing to pay would almost certainly sour relations between the two, and could lead to a legal challenge from the EU.
No deal
No deal
Boris Johnson says the UK should prepare "confidently and seriously" for a no-deal Brexit but believes the chances of it happening are "one million to one against". He says he would mitigate the effects of no-deal on the UK economy (which he admits would cause "disruption") by relying on a piece of trade law known as Article 24. He says this would allow the UK and the EU to have zero tariffs (taxes on imports) on trade while the two sides negotiated a trade deal. This would, in theory, help keep trade flowing and would stop the EU imposing tariffs on goods being imported from the UK (cars, for example, are subject to a 10% import tax from non-EU countries, and on agricultural produce it's even higher).
While accepting that a "disruptive... badly handled" no-deal Brexit would be costly, Mr Johnson said it was "vanishingly inexpensive if you prepare" and added that "much of this work has been done".
Obstacle: Boris Johnson is wrong to say Article 24 would allow for a zero tariff "standstill" with the EU, if there's no deal. To use this rule, the UK would need a trade agreement "in principle" with the EU, and leaving without a deal would imply there was no agreement. This has been pointed out by the EU trade commissioner Cecilia Malmstrom, the Bank of England governor Mark Carney and fellow Brexiteer (and Jeremy Hunt supporter) Liam Fox, the International Trade Secretary. Mr Johnson has since conceded that both sides need to agree but insists it is still an option.
Obstacle: Mr Johnson's view of the cost of a no-deal Brexit is at odds with the vast majority of economists, a significant number of his own backbenchers, and organisations such as the Office for Budget Responsibility (OBR), which calculates the government's forecasts for the economy. The OBR said no deal would push the UK economy into recession.
Jeremy Hunt
Zero tariffs
The foreign secretary says there is a prospect of doing a better deal with the EU. He is in favour of changes to the Withdrawal Agreement negotiated by Theresa May, and he thinks it is possible to get them made by 31 October. If he thinks there is a prospect of getting a deal then he is prepared to delay Brexit beyond that date. If not, he would be prepared to leave without a deal but with "a heavy heart".
Mr Johnson has said he would mitigate the effects of no deal on the UK economy (which he admits would cause "disruption") by relying on a piece of trade law known as Article 24. He originally said this would allow the UK and the EU to have zero tariffs (taxes on imports) on trade while the two sides negotiated a trade deal. This would, in theory, help keep trade flowing and would stop the EU imposing tariffs on goods being imported from the UK (cars, for example, are subject to a 10% import tax from non-EU countries, and on agricultural produce it's even higher).
Irish backstop
Obstacle: Boris Johnson was wrong to say Article 24 would automatically allow for a standstill in trade relations, and indeed - when challenged in interviews - he later accepted that it would require the agreement of both sides. Also, Article 24 only covers the trade in goods (not services) and it does not cover non-tariff barriers such as regulations. The EU has ruled out signing any Article 24 agreement immediately after a no-deal Brexit.
Mr Hunt says his aim "would be changing the backstop with some guarantees that we're not going to have a hard border on the island of Ireland for completely obvious reasons."
What is the timetable?
Obstacle: The conclusions of the EU when it decided the UK could delay leaving until the end of October, clearly state: "The European Council reiterates that there can be no opening of the withdrawal agreement." The withdrawal agreement is the legally binding part of the divorce deal, agreed by Theresa May and the EU, which contains the Irish backstop plan.
Mr Johnson has just over three months until Brexit day. He will become prime minister on 24 July and Parliament begins its summer recess the following day.
Irish border
A week later there will be a by-election and the rest of August will be pretty quiet, both in Westminster and Brussels. Parliament returns at the start of September but will take another recess later in the month for party conferences.
Mr Hunt says he will pursue "a technology-led solution" to the Irish border. He says the technology "is ready" but "the EU have not wanted to accept this kind of solution because the hope is that we might stay in this thing called the Customs Union where we have to stick to [its] tariffs". The Customs Union makes trade between EU member states easier, with no customs checks or charges on goods when they cross borders. But if the UK stayed in this kind of system after Brexit, it wouldn't be able to strike its own trade deals around the world.
On 17 October there will be a summit of EU leaders. Brexit is scheduled for 31 October, the day before the new European Commission takes office.
Obstacle: As already stated, the UK and the EU have previously looked for technological solutions to the Irish border without success. The EU deputy chief negotiator, Sabine Weyand has said she can't foresee a technological solution "in the next few years". That doesn't rule out a future fix, but it challenges Mr Hunt's view that existing technology would allow him to secure changes to the backstop by 31 October.
Negotiations:
Mr Hunt has emphasised his negotiating skills: "I'm an entrepreneur by background, I've done negotiations all my life inside government, outside government". He says the key to securing a better deal "is to put together a negotiating team for Brexit that will demonstrate to the EU that we can deliver Parliament. So what I would do differently to what we've had before is I would have the DUP in my negotiating team, I'd have the ERG who are the Brexit purists, I'd have the Scottish and Welsh Conservatives."
Obstacle: If those members of the negotiating team could agree what sort of deal they want and then negotiate it with the EU, it still would not guarantee getting the agreement through Parliament. Also, just having Northern Ireland's Democratic Unionist Party (DUP) on the negotiating team will not help with future talks with nationalists in Northern Ireland over the backstop. Sinn Fein MP Chris Hazzard described the idea as "ludicrous, and insulting to the electorate in the north".
What claims do you want BBC Reality Check to investigate? Get in touch
What claims do you want BBC Reality Check to investigate? Get in touch