The Explanation

After a shock primary win, far-right libertarian economist Javier Milei is leading polls ahead of Argentina's presidential election. He's vowing to upend the status quo. With poverty rising, inflation into triple digits and recession looming, Argentinians are divided over who to trust to lead them out of the crisis. The intensifying virulence of the debate in the already polarised political landscape makes that choice even harder.

Israel starts 'a prolonged and powerful campaign' in Gaza. What might be the consequences? BBC World Affairs editor John Simpson analyses the fallout. Also in the programme: diplomatic correspondent James Landale examines why European leaders are changing the way they tackle mass migration; senior North America reporter Anthony Zurcher explores why the United States has become increasingly ungovernable; and a BBC Eye Investigations team uncovers deadly loan apps in India and beyond. Reporter Poonam Agarwal reveals the trap ensnaring some of the world's poorest people.Produced by Pandita Lorenz and Benedick Watt

Short-term politics gets in the way of dealing with an ever-warming planet. The BBC's climate editor, Justin Rowlatt, discusses the problems with how democracies tackle climate change with the BBC's world affairs editor, John Simpson. With no victory in sight, are some leaders in Europe growing weary of supporting Ukraine? The BBC's Europe editor, Katya Adler, outlines the growing tensions inside the EU. What next for Niger now the military is in charge, and what might it mean for the region? West Africa correspondent Mayeni Jones explains what she learnt from those on the ground after gaining rare access to the country. And Armenians have fled Nogorno-Karabakh. Kian Sharifi from BBC Monitoring analyses what's at stake for neighbouring countries. Photo: Fridays for Future climate rally in Italy, Naples - 06 Oct 2023. Credit: Photo by CESARE ABBATE/EPA-EFE/REX/Shutterstock Produced by Pandita Lorenz and Benedick Watt

Now Yevgeny Prigozhin is dead, can anyone in Russia challenge President Putin’s power? BBC Russian news editor Famil Ismailov gives us his vision of the future for Ukraine.Machismo in Mexico is alive and kicking, but it looks like the country’s heading for its first female president. South America correspondent Katy Watson analyses what this might mean for women’s rights and society as a whole. Plus, after more than a decade in South Africa, BBC correspondent Andrew Harding reflects on the highs and lows and his hopes for the nation’s future.Produced by Pandita Lorenz and Ben Watt

What next for the notorious Wagner group after the plane crash that wiped out its leadership? The Russian private military group that’s left boot prints in Europe, the Middle East and Africa is facing an uncertain future. We look at official movements and narratives - in Russia and abroad - to lift the deliberate veil of murkiness and find the clues. Get in touch: theglobaljigsaw@bbc.co.ukProducer: Kriszta Satori Presenter: Krassi Twigg

Iranian women are still fighting for freedom, despite government crackdowns. World Service correspondent Faranak Amidi speaks to the BBC’s world affairs editor, John Simpson, about the fight for equality. They also discuss what has changed since Mahsa Amini's death in police custody. We also ask BBC Ukrainian editor Marta Shokalo what life is like now in Ukraine, with the war showing no sign of ending anytime soon. And how much of a threat are Chinese spies to the West? The BBC’s security correspondent, Gordon Corera, reveals how today’s espionage works.

Russia and Turkey failed to reach an agreement to bring Ukrainian grain to countries that desperately need it, at a meeting in the Black Sea resort of Sochi. What are the obstacles - and the implications for global food security? The Global Jigsaw team brings together Russia, Ukraine, Turkey, Middle East and Africa experts to assess what could happen next.

As a US territory, Puerto Rico uses the dollar, its people are US citizens and they can move freely back and forth. However, it isn’t a US state, and its residents can’t vote in presidential elections or for members of Congress.The country has a deep debt crisis, high unemployment and has experienced devastating hurricanes and earthquakes. As a result, migration to the US is common, with almost a million more Puerto Ricans in the US than on the island. In 2020, a non-binding referendum resulted in Puerto Rico voting again to become a US state. But will it ever happen?BBC Mundo’s Ronald Avila-Claudio tells us more about his homeland and what the future might hold.Presented by Claire Graham and produced by Owen McFadden for the BBC World Service.

After unilaterally declaring independence in 2008, Kosovo has been recognised by many countries, but not Serbia, which still claims it as one of its provinces. After the break-up of the former Yugoslavia in the 1990s, Serbia cracked down on Kosovo separatists, resulting in a NATO military intervention in 1999. Tensions have remained high and have begun to flare up again in recent years.The majority Albanian population mostly supports independence, but in the northern areas of Kosovo, Serbs are the majority, and many refuse to recognise Kosovan institutions. BBC Serbian reporter Aleksandar Miladinović explains these divisions, and considers if relations between the two countries can ever be normalised.

Nato members agree to support each other if they come under attack. That’s the fundamental purpose of Nato, or the North Atlantic Treaty Organization, formed in the wake of World War II. But how has its remit changed in the seven decades since its foundation? Since Russia’s invasion of Ukraine, more states have sought to join Nato, but its expansion is perceived as a threat by President Putin.James Landale, the BBC's Diplomatic Correspondent, explains how Nato works and what challenges lie ahead for the organisation.