Boris Johnson set out what he called a "conditional plan" to reopen society on Sunday night. But as BBC political editor Laura Kuenssberg says, it prompted many questions and provided only limited answers. Health correspondent Nick Triggle says  the PM is effectively trying to pull off the impossible - restart normal life, while keeping the virus at bay with limited means to do so.

Many of the moves will apply to England only after Scotland, Wales and Northern Ireland rejected No 10's new "stay alert" message, preferring to stick with "stay at home".

The prime minister insisted it was "not the time simply to end the lockdown", but people should now return to workplaces if they cannot work from home - while avoiding using public transport to get there. That has prompted an angry reaction from unions, who warn lives could be put at risk, while business groups say urgent guidance is needed. 

More outdoor exercise will be allowed - here's what we know about that so far - as will meeting one person from another household under limited circumstances. Quarantine will be introduced for those arriving in the UK by air - although passengers from France will be exempt. The PM didn't mention professional sport, but the Premier League is set to make some big decisions this week.

The next step - from 1 June - could see some primary school pupils allowed to return and some shops reopened. A tentative restarting of the hospitality industry could also be possible from July. Much depends on what happens to the crucial R number, so find out more on that .

Here's a fuller explanation of how lockdown will look now. Much more detail will be published later, but Mr Johnson can expect a tough time when he appears before MPs this afternoon, with Labour leader Sir Keir Starmer leading the criticism.

The UK follows other nations in easing some of its restrictions, but in a number there are fears of a possible coronavirus second wave. Overall, China continues to see low numbers of infections, but it reported 17 new cases on Monday and there is growing concern over a cluster in north-eastern Shulan city in Jilin province. 

In South Korea, renewed restrictions have been imposed after a series of new transmissions linked to Seoul's nightlife district. And in Germany, official data shows the infection rate has risen after lockdown was eased.

Despite those concerns, France and Spain are set for a relaxation this week. All Australians will soon be allowed to visit friends and family and schools are starting to reopen. New Zealand continues to take similar steps, while India is resuming some train services. 

In the US, the death toll is approaching 80,000. New York - the epicentre of the country's outbreak - is weighing options for relaxing lockdown measures, but the situation in care homes is a particular concern.

See all the latest from around the world in our live page.

Visits to care homes have been banned across the world, but one centre in the Netherlands has found a way to bring people together using glass pods. Find out more. That's just one example of the efforts people are making to keep up human connections despite social distancing. Here we round up some more, including the teacher making "plastic hugs". And with the psychological toll of coronavirus becoming clear, read about the efforts being made in Italy to help survivors cope with the sort of mental health effects typically associated with disasters or war.

Many papers are deeply frustrated by the prime minister's address. The Sun's political editor describes the "stay alert" message as "feeble" and the PM himself as "paralysed by indecision". The Guardian thinks he has left Britain "confused and divided". As columnist Simon Jenkins puts it: "Boris Johnson says we can be a little less careful, while still being extremely careful." The Daily Mirror has a similar assessment, calling the new messaging "confusing and potentially catastrophic". The Daily Telegraph's leader is more sympathetic though. "The lockdown cannot continue for ever," it says, "and all the prime minister is urging people to do is use their common sense". Sketchwriter Quentin Letts, in the Times, thinks the address had a "daunting air", but those hoping for a list of lifted restrictions will have been disappointed.

From elsewhere

The Food Chain, from BBC World Service, wonders what's next for restaurants after such a torrid time. And in Radio 4's More or Less, Tim Harford explains why it's so hard to work out the Covid-19 fatality rate.

Like so many events, this year's Eurovision Song Contest fell victim to coronavirus. BBC Newsbeat brings you the inside story on the cancellation from the artists who were due to sing. Elsewhere, what happens when an internet troll meets one of the people he abuses? Find out. And in this week's The Boss, we speak to the men behind the high-flying circus firm loved by rock and pop royalty.