In Jesse Armstrong’s squirminglyfunny satire, four tech moguls gather at a retreat called Mountainhead (a wry nod to Ayn Rand’s paean to individualism The Fountainhead). When the launch of a deep-fake tool by Cory Michael Smith’s billionaire Venis plunges the world into financial and social meltdown, he and his alpha male peers – Jeff (Ramy Youssef), Randall (Steve Carell) and their host Souper (Jason Schwartzman) – insouciantly ponder exploiting this “moment of creative destruction” and taking over the world. As in Succession, Armstrong has a keen eye for the supercilious world of the super-rich, where people are expendable and petty grievances can be dressed up as utopianism.Sunday 1 June, 9pm, Sky Atlantic
Part affectionate throwback to classic Agatha Christie, part knowing sendup, Tom George’s engagingcomic whodunnitis set in the wake of a murder after the 100th West End performance of The Mousetrap in 1953. The corpse is lecherous American director Leo Kopernick (Adrien Brody), who was due to film a version of the play. Sozzled Insp Stoppard (Sam Rockwell) and eager, naive PC Stalker (Saoirse Ronan) are put on the case, with a star-stuffed cast of suspects – Ruth Wilson, David Oyelowo, Reece Shearsmith, Harris Dickinson – joining in the fun.Saturday 31 May, 9.20pm, Channel 4
Pete Docter’s relentlesslyinventive animationspins a touching yarn out of the competing emotions that swirl around a child’s brain. Joy (a chipper Amy Poehler) is the controlling voice in the head of 11-year-old Riley. But when the girl and her parents move to a big city, San Francisco, the other feelings – Anger, Fear, Disgust, but principally Phyllis Smith’s Sadness – come into play. An error in the handling of core emotions sends Joy and Sadness on a desperate quest into the weirder recesses of Riley’s mind to save their charge in a bitter, sweet tearjerker.Sunday 1 June, 3.30pm, BBC One
Tommy Lee Jones always appears most at home on screen with a stetson, a horse and a noble purpose. For this rare2005foray into directing, he gave himself a plum role as Texas ranch foreman Pete, who is determined to honour the last wishes of his friend and colleague, illegal immigrant Melquiades (Julio Cedillo), shot dead by trigger-happy border patrolman Mike (Barry Pepper). A modern western with a social conscience and a dose of mordant wit, it also has time for those genre staples of self-sufficiency, friendship and loyalty.Sunday 1 June, 9pm, Great! Action
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A woman who lived her life battling the repression that is an enduring theme in her novels, Irish author Edna O’Brien is a terrific subject for a documentary. Sinéad O’Shea does her proudhereand is blessed with access to the then 93-year-old – who is as sharp as ever when talking through her experiences. But O’Brien is also tinged with melancholy – a result of a traumatic childhood, an oppressive marriage and the misogynist resentment she faced – not least back in Ireland – due to her frank opinions.Sunday 1 June, 9pm, Great! Action
Armando Iannucci’s2009 comedybridges the gap between The Thick of It and Veep by throwing together governmental fools and chancers from the UK and US. It also ups the ante by making the result of the bungling of its apparatchiks, spin merchants and elected officials an actual war. Most of the Thick of It cast return, though confusingly as different characters. Luckily, Peter Capaldi’s vituperative director of comms Malcolm Tucker is present and incorrect, bullying the out-of-his-depth minister for international development Simon Foster (Tom Hollander) on an ill-fated visit to Washington DC.Tuesday 3 June, 11.45pm, BBC Two
New Mexico casual labourer Dylan (Charlie Plummer) is getting by day to day with his alcoholic mother and younger brother, until he gets a casual job at the House of Splendor ranch. It is home to – and refuge for – a community of LGBTQ+ folk, in particular rodeo rider Sky (Eve Lindley). Her and Dylan’s mutual attraction is instant, though she is already in a relationship that maybe isn’t as open as she says and he hopes. Luke Gilford’s queercoming-of-age dramais a warm-hearted tale of finding your people, set in a bigotry-free environment that keeps the political personal.Wednesday 4 June, 11.20pm, Film4