BBC

Xi Jinping and Donald Trump have held their first face-to-face talks in six years in a moment of high trade tension between China and the US.

Mr Trump hailed an "amazing" meeting with his Chinese counterpart, but Beijing was less effusive. Thursday's talks did not lead to a formal agreement but the announcements suggest they are closer to a deal. We'll try to work out what has been sorted out at the talks in South Korea.

Also in the programme: The latest mass killings in Sudan spark international outrage, with the RSF rebel leader promising an immediate investigation into the actions of his troops; the Dutch election is a neck-and-neck race between centrist liberals and anti-Islam populists; and five more suspects have been arrested over the Louvre museum jewellery heist.

(Photo shows US president Donald Trump and Chinese president Xi Jinping shake hands in Busan, South Korea on 30 October 2025. Credit: Yonhap/EPA)

Why has the Gambian government issued a strong warning to ex -President Yahya Jammeh following his announcing plans to return from 9 years in exile?.

 

Nigeria, South Africa, Mozambique, and Burkina Faso removed from a global money-laundering watchlist. How can they benefit?

 

And how years of drought is decimating wealth, and thousands of lives in the  self-declared Republic of Somaliland. 

 

 

Presenter: Nyasha Michelle

Producers: Yvette Twagiramariya, Stefania Okereke and Mark Wilberforce in London.

Technical Producer: Chris Kouzaris

Senior Producer: Paul Bakibinga

Editors: Alice Muthengi and Andre Lombard.

Also, 4 people arrested over unprovoked racist assault on tourists in Belfast city centre

Melvyn Bragg and guests discuss the dance which, from when it reached Britain in the early nineteenth century, revolutionised the relationship between music, literature and people here for the next hundred years. While it may seem formal now, it was the informality and daring that drove its popularity, with couples holding each other as they spun round a room to new lighter music popularised by Johann Strauss, father and son, such as The Blue Danube. Soon the Waltz expanded the creative world in poetry, ballet, novellas and music, from the Ballets Russes of Diaghilev to Moon River and Are You Lonesome Tonight. With Susan Jones Emeritus Professor of English Literature at the University of Oxford Derek B. Scott Professor Emeritus of Music at the University of Leeds And Theresa Buckland Emeritus Professor of Dance History and Ethnography at the University of Roehampton Producer: Simon Tillotson Reading list: Egil Bakka, Theresa Jill Buckland, Helena Saarikoski, and Anne von Bibra Wharton (eds.), Waltzing Through Europe: Attitudes towards Couple Dances in the Long Nineteenth Century, (Open Book Publishers, 2020) Theresa Jill Buckland, ‘How the Waltz was Won: Transmutations and the Acquisition of Style in Early English Modern Ballroom Dancing. Part One: Waltzing Under Attack’ (Dance Research, 36/1, 2018); ‘Part Two: The Waltz Regained’ (Dance Research, 36/2, 2018) Theresa Jill Buckland, Society Dancing: Fashionable Bodies in England, 1870-1920 (Palgrave Macmillan, 2011) Erica Buurman, The Viennese Ballroom in the Age of Beethoven (Cambridge University Press, 2022) Paul Cooper, ‘The Waltz in England, c. 1790-1820’ (Paper presented at Early Dance Circle conference, 2018) Sherril Dodds and Susan Cook (eds.), Bodies of Sound: Studies Across Popular Dance and Music (Ashgate, 2013), especially ‘Dancing Out of Time: The Forgotten Boston of Edwardian England’ by Theresa Jill Buckland Zelda Fitzgerald, Save Me the Waltz (first published 1932; Vintage Classics, 2001) Hilary French, Ballroom: A People's History of Dancing (Reaktion Books, 2022) Susan Jones, Literature, Modernism, and Dance (Oxford University Press, 2013) Mark Knowles, The Wicked Waltz and Other Scandalous Dances: Outrage at Couple Dancing in the 19th and Early 20th Centuries (McFarland, 2009) Rosamond Lehmann, Invitation to the Waltz (first published 1932; Virago, 2006) Eric McKee, Decorum of the Minuet, Delirium of the Waltz: A Study of Dance-Music Relations in 3/4 Time (Indiana University Press, 2012) Eduard Reeser, The History of the Walz (Continental Book Co., 1949) Stanley Sadie (ed.), The New Grove Dictionary of Music and Musicians, Vol. 27 (Macmillan, 2nd ed., 2000), especially ‘Waltz’ by Andrew Lamb Derek B. Scott, Sounds of the Metropolis: The 19th-Century Popular Music Revolution in London, New York, Paris and Vienna (Oxford University Press, 2008), especially the chapter ‘A Revolution on the Dance Floor, a Revolution in Musical Style: The Viennese Waltz’ Joseph Wechsberg, The Waltz Emperors: The Life and Times and Music of the Strauss Family (Putnam, 1973) Cheryl A. Wilson, Literature and Dance in Nineteenth-century Britain (Cambridge University Press, 2009) Virginia Woolf, The Voyage Out (first published 1915; William Collins, 2013) Virginia Woolf, The Years (first published 1937; Vintage Classics, 2016) David Wyn Jones, The Strauss Dynasty and Habsburg Vienna (Cambridge University Press, 2023) Sevin H. Yaraman, Revolving Embrace: The Waltz as Sex, Steps, and Sound (Pendragon Press, 2002) Rishona Zimring, Social Dance and the Modernist Imagination in Interwar Britain (Ashgate Press, 2013)

Donald Trump and Xi Jinping have met for the first time since 2019 to discuss a possible truce in the US-China trade war. The leaders of the world's two biggest economies shook hands and spoke of friendship ahead of the "amazing" meeting in South Korea. President Trump said they agreed a cut in tariffs and a rare earth minerals deal. Also: the US says it will begin testing its nuclear weapons to keep up with Russia and China; Hurricane Melissa moves towards the Bahamas and Cuba after causing unprecedented devastation in Jamaica; Brazil's president condemns the police raid that killed more than 130 people in Rio de Janeiro; the long lost wolf spider is re-discovered in the UK; what drives those who want to live forever; and the art of presidential gift giving.

How Jihadists wrestle with the question: to use or not to use. The allure of this powerful tool and the damage they fear it could inflict on their image and reputation. Supporters of the Islamic State group tend to be early adopters of new tech, and some have already experimented with generative Artificial Intelligence. But that has exposed deep divisions in jihadist circles. The Global Jigsaw explores this debate to understand what “responsible AI” means for them.

The much-anticipated meeting between Donald Trump and China’s President Xi Jinping takes place in Korea. Presenter Sam Fenwick hears from both sides ahead of a crucial talks between the two leaders.

The owner of a US based coffee roastery based in New York talks to us about the how his business is coping with the fallout from the global tariff war.

Microsoft, Alphabet and Meta all release their latest quarterly numbers. They make up around 15 per cent of the S&P 500. We find out how well these tech giants have done, and what challenges they face in the future.

US President Trump will meet his Chinese counterpart Xi Jinping for the first time since returning to the White House in the coming hours. President Trump has said he expects to agree a deal to ease trade tensions between the two economic rivals. We hear from a Chinese economist and US congressman.

Also on the programme: a report from Rio where police raids on drugs gangs have killed more than 130 people. And we have the latest as the Chancellor Rachel Reeves admits breaking housing rules by unlawfully renting out her family home without a licence.

The right-wing governor of Rio state in Brazil has praised Tuesday's controversial anti-gang operation, in which more than a-hundred and thirty people were killed. Claudio Castro said the only victims were the four police officers who died. Two- and- a half thousand police and soldiers took part in the raids against the Red Command. Major gun battles erupted in two Rio favelas in the biggest security operation in the history of Rio state. Brazil's centre-left President Luis Inacio Lula da Silva said he was surprised an operation of this scale was set up without the knowledge of the federal government.

Also in the programme: the Netherlands head to the polls; and a deep dive into presents for US Presidents.

(Photo: Mourners react as people gather around bodies. CREDIT: REUTERS/Ricardo Moraes)

Freddie makes a significant gesture, and Pip receives a helping hand.