Could seaborne sabotage bring down the internet? Will Labour dare to replace the council tax? And how can we help ex-prisoners find a home? Olly Mann and The Week delve behind the headlines and debate what really matters from the past seven days. With Holden Frith, Julia Macfarlane and Irenie Forshaw.Image: David Oller / Europa Press / Getty Images

Have we made a breakthrough in the battle against sepsis? Are MPs treating their jobs with due respect? And are some Olympic athletes not all they seem? Arion McNicoll and The Week delve behind the headlines and debate what really matters from the past seven days. With Harriet Marsden, Rebekah Evans and Abdulwahab Tahhan. Olly Mann will return next week

What stopped Barack backing Kamala? Is the world going cold on online casinos? What can we do now to fund life after work?  Arion McNicoll and The Week delve behind the headlines and debate what really matters from the past seven days. With Rebecca Messina, Suchandrika Chakrabarti and David Runciman. Olly Mann will return in two weeks

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 MarsdenImage: 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 prideOlly 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