Overnight, the US president Donald Trump announced on his social media platform, TruthSocial, that Israel and Iran had negotiated a ceasefire. The deal, which was reportedly struck with Qatari assistance, was subsequently acknowledged by Iran. But it remains unclear when the ceasefire is supposed to begin, and since the US president’s announcement, the two adversaries have continued to hit each other with missiles. Four Israelis are reported to have been killed in Iranian missile strikes, while Iran reported "intense" Israeli bombardment of Tehran.

Trump is scheduled to be attending the annual Nato leaders’ summit in the Hague which begins today. The key meeting of the slimmed down two-day gathering will be tomorrow when leaders meet to discuss, and most likely affirm, their commitment to raise their countries’ defence budgets to 5% of GDP. International security analyst Stefan Wolff writes that, with the president’s mind still apparently on the Middle East, much of the leaders’ energy will be focused on keeping Trump engaged with Nato amid fears the US president could significantly scale down US commitment, or even walk away from the alliance.

If you’ve woken up in the past few days feeling groggy and like you’ve only just nodded off, you aren’t alone. This useful article looks at exactly what the light and heat of summer does to our sleep patterns – and how you can try to maximise your shuteye.

And it’s a well-worn cliche that the British embarrass easily (in fact, studies have shown that it’s a pretty universal feeling no matter where you are). But there are quite a few evolutionary reasons why embarrassment can actually be quite useful.