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In 1962 the world teetered on the edge of nuclear destruction as the Presidents of the USA and the Soviet Union fought over Soviet warheads installed on the islands of Cuba. In Nuclear Folly: A New History of the Cuban Missile Crisis, the historian Serhii Plokhy retells the tortuous decision-making and calculated brinkmanship of John F Kennedy, Nikita Khrushchev and Fidel Castro. He tells Amol Rajan it was ultimately fear that saved the planet, and it’s time to draw lessons from the many mistakes that were made at the time.The Cold War era did produce a nuclear arms-control agreement – the Intermediate-Range Nuclear Forces Treaty – signed in 1987. But the nuclear physicist and former director of the UN Institute for Disarmament Research Patricia Lewis says that in 2019 the United States and Russia withdrew their support. Lewis, who now leads the International Security programme at Chatham House, asks whether we are now entering a second nuclear age.The BBC journalist Sarah Rainsford visited the sites of the Soviet Union's nuclear stations in Cuba when she was posted there in 2011. She wrote about her experiences and the end of the Castro era in Our Woman in Havana. Rainsford is now the BBC’s Moscow correspondent and explores how far Khrushchev’s political scheming and disinformation compare to the strategy of President Putin.Producer: Katy Hickman

Reports of a mental health epidemic among young people both leading up to and during the pandemic are now widespread. Sally Holland is the Children’s Commissioner for Wales and a former social worker. She tells Andrew Marr that mental health services in Wales, and the rest of the UK, need a serious rethink, because too many children are waiting too long for help.But the health researcher and psychologist Lucy Foulkes asks whether we have become fixated with labelling the stresses and challenges of human experience as a mental disorder. In Losing Our Minds she explains what is known about mental health problems, and why they so often appear during adolescence. But she argues that it’s vitally important to distinguish between ‘normal’ suffering and actual illness. Defining what is and isn’t an illness is also the subject of Suzanne O’Sullivan’s latest book The Sleeping Beauties – And Other Stories of Mystery Illness. Here the neurologist looks at startling cases of what appear to be psychosomatic illnesses which have infected groups of people – from refugee children in Sweden unable to wake up, to American high school students having seizures, to mass headaches and memory loss in the US embassy in Cuba. O’Sullivan looks at how far these disorders are influenced by societal forces and human biology.Producer: Katy Hickman

Tom Tugendhat MP is the Conservative chair of the Foreign Affairs Committee. He tells Andrew Marr that he’s very much focused on British foreign policy priorities after Brexit. But the government’s new Trade Bill is facing opposition from those insisting that human rights abuses must be investigated before any deals are done. The MP for Tonbridge and Malling also highlights the need to be more aware of China’s economic ambitions and global role. Geeta Tharmaratnam is keen that more focus should be placed on Africa. As a venture capitalist and CEO of an investment company she see huge economic possibilities across the continent, especially in relation to African women entrepreneurs. She looks more closely at the African Continental Free Trade Area which was signed by a majority of countries in Kigali, Rwanda in 2018 and came into force this year.But the journalist Michela Wrong questions whether the Rwandan government, and especially its much feted leader President Paul Kagame can be trusted. Following the civil war and genocide in 1994 Kagame became vice-President and then leader of his country. He has prioritised national development and been successful in securing international aid, but Wrong follows the story of his rise to power and argues that he has overseen a regime intent on political repression.Producer: Katy Hickman