Explainer: What led to the latest stalemate - and what happens next?
Why does Boris Johnson want the backstop removed from the Brexit Withdrawal Agreement?
In his letter to EU chiefs, Mr Johnson underlined three reasons he believes the backstop must go.
He argued it is "anti-democratic and inconsistent with the sovereignty of the UK". He said it is "inconsistent with the UK's desired final destination for a sustainable long-term relationship with the EU". And he said the backstop "risks weakening the delicate balance embodied" by the Good Friday Agreement.
Isn't the backstop about protecting the Good Friday Agreement?
The Irish Government, with the backing of the EU, has insisted the only purpose of the backstop is to maintain the status quo.
It says an open Border and the all-island economy can only be retained if there is regulatory alignment between Northern Ireland and the Republic.
The UK government has promised not to erect a hard Border, so what is the alternative to the backstop?
The prime minister said the UK would agree to a "legally binding commitment" not to put in place infrastructure, checks or controls at the Border with Ireland and would hope the EU did the same. The backstop should be replaced with a commitment to put in place "alternative arrangements".
What are the alternative arrangements?
We simply don't know. Mr Johnson says they should be in place "as far as possible before the end of the transition period", which was supposed to last 21 months.
However, he hasn't outlined what they might be. Mr Johnson said the UK is "ready to look constructively and flexibly at what commitments might help".
What is the response from the EU?
Ireland has already rejected the idea of scrapping the backstop "unless and until" alternative ways of keeping the Border open are found.
It says it is an insurance policy needed to protect peace. This position is entirely backed by the EU. In a hard-hitting statement, EU Council President Donald Tusk said those who are against the backstop are supporting the re-establishment of a Border "even if they do not admit it".
So what happens next?
Mr Johnson will meet German Chancellor Angela Merkel today and France's Emmanuel Macron tomorrow - but the stalemate looks set to continue. Meanwhile, both sides continue to ramp up no-deal preparations.