We are away for Christmas, so this is a repeat of a previous episode.

Donald Trump has spent this year trying to negotiate a deal to end the war in Ukraine. So far, Vladimir Putin doesn’t seem interested in the US’ proposals.

One man who has experience successfully negotiating with Russia – and many other American adversaries – is Roger Carstens, former Special Presidential Envoy for Hostage Affairs. From 2020 to 2025 he worked to free dozens of US citizens taken hostage and wrongfully detained around the world, including Russia. Securing their release often required complex deals that took years to put together.

What does it take to successfully negotiate with Vladimir Putin’s Russia?

Producer: Lucy Pawle

Executive producer: James Shield

Senior news editor: China Collins

Mix: Travis Evans

Photo: Roger Carstens. Credit: BBC

We are away for Christmas, so this is a repeat of a previous episode.

AI companies are seeing a monumental surge in investment – but some experts are now warning of the risks of an economic bubble.

Could AI be the biggest market bubble since the dot-com crash? Or is it a genuinely transformative technology that’s simply taking time to deliver? We speak to the BBC’s Evan Davis.

Producers: Aron Keller and Xandra Ellin

Executive Producer: James Shield

Mix: Travis Evans

Senior news editor: China Collins

Photo: Artificial Intelligence mobile apps. Hannibal Hanschke/EPA/Shutterstock

We are away for Christmas, so this is a repeat of a previous episode.

In 1994, Ukraine surrendered the world's third-largest nuclear arsenal, inherited from the collapsed Soviet Union, in exchange for security assurances from the US, Russia, and the UK.

Ukraine’s denuclearisation is often considered a huge success story in nuclear non-proliferation, but in retrospect, it may have paved the way for Putin's 2022 invasion.

As talk of US-European security guarantees for Ukraine resurfaces in the context of tentative Russia-Ukraine peace talks, we speak with BBC Paris correspondent Andrew Harding about the history of the 1994 agreement, and consider whether Ukraine would ever again believe promises made to protect it.

Producers: Sam Chantarasak and Xandra Ellin

Executive producer: Annie Brown

Mix: Travis Evans

Senior news editor: China Collins

Photo: France's President Emmanuel Macron and Ukraine's President Volodymyr Zelensky. Ludovic Marin/ Getty

We are away for Christmas, so this is a repeat of a previous episode.

Apple is promising to make more products in the US, backed by a $600bn investment over the next four years. But after decades of relying on Chinese manufacturing that promise is going to be tough to keep.

Today we’re joined by journalist and author Patrick McGee to discuss whether Apple can navigate the demands of Donald Trump’s America First agenda and disentangle itself from a made-in-China business model.

Producers: Hannah Moore and Aron Keller

Executive producers: James Shield and Annie Brown

Mix: Nicky Edwards and Travis Evans

Senior news editor: China Collins

Photo: Apple CEO Tim Cook. Manuel Orbegozo/Reuters

We are away for Christmas, so this is a repeat of a previous episode.

For much of the 21st century, our social lives have been shaped, at least in part, on the internet. But in an age of influencers, generative AI, complex algorithms, and politically entangled technocrats, some users say social media is growing less, well, social.

So, is social media dead? Or is it just becoming something else? We speak with New Yorker staff writer Kyle Chayka about what happened to social networks, and what their transformation suggests about the future of media.

Producers: Xandra Ellin and Aron Keller

Executive Producer: James Shield

Mix: Travis Evans

Senior News Editor: China Collins

Photo: Social media apps on a phone. Yui Mok/PA

We are away for Christmas, so this is a repeat of a previous episode.

In September, President Trump and the U.S. Health Secretary Robert F. Kennedy Jr. held a press conference in which they made extraordinary new claims about autism. They suggested a potential link between the use of Tylenol during pregnancy and the development of autism. They also advocated spacing out childhood vaccinations.

The science journalist Adam Rutherford explains to the Global Story how the Wakefield vaccine conspiracy became the biggest medical disinformation disaster in recent history, and how these ideas found fertile ground in the Trump administration.

Producers: Viv Jones, Valerio Esposito

Executive producer: Annie Brown, James Shield

Mix: Travis Evans

Senior news editor: China Collins

Photo: President Trump & Robert F. Kennedy Jr. Kevin Lamarque/Reuters

Attacks by Jewish settlers on Palestinians in the occupied West Bank have broken UN records this year, reaching the highest level in almost 20 years.

Israel’s Prime Minister Benjamin Netanyahu has blamed a “minority” that “does not represent the large settler public”. Meanwhile, Israel’s security cabinet has just approved the recognition of 19 new settlements as the government continues its settlement expansion push.

Executive Producer: Bridget Harney

Mix: Marty Peralta

Senior news editor: China Collins

Photo: Israeli border police remove settlers near Hebron. Credit Abir Sultan/EPA-EFE/REX/Shutterstock.

Tensions between the US and Venezuela are reaching a dangerous tipping point. The Trump administration has accused president Nicolas Maduro of leading a drug cartel and declared Maduro's government a “foreign terrorist organisation”. President Trump has also ordered a naval blockade of the country’s oil-sanctioned exports using what he calls “the largest ever armada assembled in the history of South America”.

In today’s episode, we speak to BBC Mundo journalist, Jorge Perez Valeri to ask whether the escalating military rhetoric from Washington could be paving the way for war, and how Venezuelans, already grappling with deep economic hardship, are feeling about the prospect.

The promise of pore-free, glassy, youthful-looking skin has made Korean beauty products a global phenomenon. Americans spent as much $1.7bn (£1.3bn) on K-beauty in 2024, according to industry estimates, and the US now imports more cosmetics from South Korea than any other country.

How did the South Korean government help K-beauty ride the soft power wave that has also brought us TV shows like KPop Demon Hunters, and pop groups such as Blackpink and BTS? And what are the risks of buying into the ‘perfect’ beauty ideals that the industry promotes?

Today, we speak to Elise Hu, the host of TED Daily Talks host and author of 'Flawless: Lessons in Looks and Culture from the K-Beauty Capital'.

Producer: Hannah Moore

Executive producer: Bridget Harney

Mix: Marty Peralta

Senior news editor: China Collins

Photo: Model Lee Hyun-yi attends the photocall event celebrating the launch of AHC’s new product ‘Full Lift Eye Cream for Face’ at the FKI Tower Conference Center in Yeouido, Yeongdeungpo-gu. Credit: iMBC/Imazins via Getty Images.

After the Port Arthur massacre in 1996, Australia tightened its gun laws, and has since been considered a world-leading example by gun control advocates of how to lessen the chances of mass shootings occurring.

However, the mass murder of at least 15 people in an antisemitic attack at Bondi beach on Sunday has again raised the issue of gun access, and Australian prime minister Anthony Albanese has said he is “ready to fight” to strengthen the laws again.

On today’s show, Ariel Bogle, an investigations reporter with Guardian Australia, explains why the number of guns in Australia has been rising, and how stricter laws might be received in the country.

Producers: Hannah Moore and Xandra Ellin

Executive producer: James Shield

Mix: Marty Peralta

Senior news editor: China Collins

Photo: Photo of unregistered handguns that were returned to police, near Smederevo, Serbia. Credit: Dimitrije Goll /EPA-EFE/REX/Shutterstock