Are Donald Trump's legal obstacles melting away? Could self-testing replace the cervical smear? And what kind of world is Katy Perry living in? Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Holden Frith, Leaf Arbuthnot and Jamie Timson

Will Trump follow a conservative plan for a dystopian future? What is happening on the island of Diego Garcia? And how will humans fare on the red planet?

Image: Erik McGregor / LightRocket via Getty Images

Will unrest in Turkey derail a deal with Syria? How prepared is the world for bird flu? And could AI exacerbate climate change? Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Abdulwahab Tahhan, Arion McNicoll and Harriet Marsden

Image: Bakr Alkasem/AFP/Getty Images

How dangerous to our health are aircraft exhaust fumes? Why is Airbnb being banished from Barcelona? And are Ukrainians really less stressed than Brits? Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Jess Hullinger, Irenie Forshaw and Holden Frith

Why are Les Bleus speaking out about the French election? What's making people turn off the news? And should TikTok and Instagram carry health warnings? Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Rebekah Evans, Jamie Timson and Abdulwahab Tahhan

The Edinburgh Fringe is the latest cultural event to be drawn into a row around funding from companies linked to Israel and fossil fuels. But where other organisers have severed their ties, the Edinburgh Festival Fringe Society has robustly defended their sponsorship deal with the investment firm Baillie Gifford. Are they right, and is the tide turning against disinvestment?

Plus: a vice-presidential plane crash and woeful weather. Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Jamie Timson, Mariana Vieira and Leaf Arbuthnot.

The Marubo people, who live in the Amazon rainforest, are one of the most isolated societies in the world – and, until recently, it was entirely offline. When Elon Musk's Starlink brought the web to their villages, the impact was profound.

Plus: anonymity for sex-crime suspects, and a bad day for French pride

Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Harriet Marsden, Emma Smith and Rebecca Messina

A week after a landslide that left hundreds of people dead, the prime minister of Papua New Guinea is facing a vote of no confidence. The outcome will be keenly watched in China, Australia and the US, which are seeking to woo the country's government and solidify their influence in the Pacific.Plus: a helicopter scandal at the MoD and the rebirth of Loaded magazine.Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Mariana Vieira, Harriet Marsden and Holden Frith.

This week the Vatican is playing host to an international conference on climate change, at which many of the world's mayors and governors will discuss how we can adapt to the challenges of global warming. Could religious leaders help to win over some people who wouldn't listen to politicians?

Plus: ultra-long mortgages and Swiftonomics.

Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Jessica Hullinger, Guy Anker and Cindy Yu.