This nebulous study of Luigi Mangione veers close to romanticising him as a latter-day Robin Hood

On 5 December 2024, the New York Times ran the headline “Insurance CEO Gunned Down In Manhattan”. The newspaper then noted that Brian Thompson was “shot in the back in Midtown Manhattan by a killer who then walked coolly away”. The murder in broad daylight was indeed both cold and shocking. But many Americans had a different response: for those who had been denied health insurance or faced exorbitant healthcase costs, the news felt cathartic. Social media blew up. One post read: “All jokes aside … no one here is the judge of who deserves to live or die. That’s the job of the AI algorithm the insurance company designed to maximize profits on your health.”

Five days later, Luigi Mangione, a good-looking, 26-year-old University of Pennsylvania graduate with a master’s in computer science, was apprehended at a McDonald’s in Altoona, Pennsylvania. He awaits trial on federal and state charges of murder, with prosecutors seeking the death penalty. So who is Mangione? And what might have motivated the alleged crime? These are the questions John H Richardson attempts to answer in an investigation that explores broader themes, too.

Hamad thinks his method enhances the flavour. Lucia says he’s breaking all the sacred rules. Who needs to wake up and smell the coffee?

• Find out how to get a disagreement settled or become a juror

Hamad’s method isn’t the way it’s supposed to be done. I’m Italian – I know all about good coffee

Pressing down the grounds improves the flavour. Lucia is just being a coffee snob

An enraged behemoth breaks free from a government black site bent on revenge, but there is not much here aside from some monster action

‘We’re going to need more wallpaper” turns out to be the Nordic answer to “We’re going to need a bigger boat”, after a 50-metre troll has just swept a leg through someone’s soon-to-be-renovated house. When the quips revolve around interior design, you know Norwegian big-budget film-making is taking a softer path than its raucous American inspirations.

This is a Netflix sequel to Norwegian horror comedy Troll with the original director Roar Uthaug returning, and home is clearly a theme dear to the franchise’s heart. The first film’s Scandi-kaiju was returning to its roots, on a mission to trash Oslo. But the new “megatroll” – looking like Danny McBride in the throes of a full-body fungal infection – is headed for Trondheim, bent on revenging itself on the nation’s founding father and chief troll-scourge, King Olaf. Trollogist Nora (Ine Marie Wilmann) and ministerial adviser Andreas (Kim Falck) return, again trying to hold the authorities back from simply lighting up the enraged behemoth after it escapes from a government black site.

This week’s best wildlife photographs from around the world

US group Dekleptocracy identifies chemicals used for military vehicles’ lubricants and tyres as potential vulnerabilities

A US group has identified several obscure but potentially key sanctions it says could seriously disrupt Russia’s war effort in Ukraine after last month’s targeting of the Kremlin’s biggest oil firms.

Previous rounds of sanctions have been applied to Russian energy companies, banks, military suppliers and the “shadow fleet” of ships carrying Russian oil.

Anastasia Samoylova took a photographic journey up the US east coast – and found herself in America’s unreconciled past just as much as its fragmented present

A series of walking festivals and cultural programmes aim to lure visitors to the Algarve’s woodland interiors and pretty villages to help boost tourism year round

‘I never mind doing the same walk over and over again,” said our guide, Joana Almeida, crouching beside a cluster of flowers. “Each time, there are new things – these weren’t here yesterday.” Standing on stems at least two centimetres tall and starring the dirt with white petals, the fact these star of Bethlehem flowers sprung up overnight was a beautiful testament to how quickly things can grow and regenerate in this hilly, inland section of the Algarve, the national forest of Barão de São João. It was also reassuring to learn that in an area swept by forest fires in September, species such as strawberry trees (which are fire-resistant thanks to their low resin content) were beginning to bounce back – alongside highly flammable eucalyptus, which hinders other fire-retardant trees such as oak. Volunteers were being recruited to help with rewilding.

Visitor numbers to the Algarve are growing, with 2024 showing an increase of 2.6% on the previous year – but most arrivals head straight for the beach, despite there being so much more to explore. The shoreline is certainly wild and dramatic but the region is also keen to highlight the appeal of its inland areas. With the development of year-round hiking and cycling trails, plus the introduction of nature festivals, attention is being drawn to these equally compelling landscapes, featuring mountains and dense woodlands. The Algarve Walking Season (AWS) runs a series of five walking festivals with loose themes such as “water” and “archaeology” between November and April. It’s hoped they will inspire visitors year round, boosting the local economy and helping stem the tide of younger generations leaving in search of work.

Number of women incarcerated around the world rising at nearly three times the rate of men, with female prisoners often subjected to sexual violence and forced labour

• Explainer: How many women are in prison and on death row around the world? – in charts

Up to a million women worldwide are facing sexual violence and forced labour in prisons, where they are overlooked and forgotten, in what is being called a growing global crisis.

The number of incarcerated women is rising much faster than men and is expected to surpass one million on current trends. While on average women account for between 2% and 9% of national prison populations, since 2000 the number imprisoned has grown by 57%, compared with a 22% increase in the men’s prison population.

The reader grapples with fascism and complicity through the eyes of a mute autistic girl being treated during the second world war

As I started reading Alice Jolly’s new novel, whose narrator is a mute autistic girl in wartime Vienna, I realised that I was resisting its very premise. I am generally sceptical about books that use child narrators to add poignancy to dark plots, or novels that use nazism as a means of introducing moral jeopardy to their characters’ journeys. And yet by the end Jolly had won me over. This is a book that walks a tightrope between sentimentality and honesty, between realism and imagination, and creates something spirited and memorable as it does so.

We meet our fierce narrator, Adelheid Brunner, when she is brought into a children’s hospital by her grandmother, who cannot cope with the little girl’s fixations. Adelheid is obsessed with the matchboxes of the title, which she is constantly studying, ordering and occasionally discarding. In the hospital, she finds that she and her fellow child inmates are the object of obsessive study in turn by their doctors – sometimes understood, sometimes valued, and then, tragically, sometimes discarded.

President calls the shooting in Washington an ‘act of terror’, as officials name Rahmanullah Lakanwal as suspected shooter

Donald Trump has called for his government to re-examine every Afghan immigrant who entered the US during Joe Biden’s administration, after law enforcement officials identified the suspect in the shooting of two national guard members in Washington as a man from Afghanistan.

A statement from the Department of Homeland Security named the suspect asRahmanullah Lakanwal, a 29-year-old Afghan national who entered the US under a Biden-era policy allowing Afghans set up after the US withdrawal from Afghanistan in 2021. Immigration authorities granted Lakanwal asylum earlier this year, according to CNN.

New players have come in, too many of them, and has meant a dilution of the collective will instilled by Klopp

Before this game Arne Slot had announced that he was “almost confused”. Which does at least raise some tantalising questions. Mainly, what is this Liverpool team going to look like when he gets there, when a state of full confusion is finally attained, when even Slot’s confusion stops being confusing and reveals its diamond-cut final form.

Britain’s most successful female UFC fighter on knowing when to stand her ground, why she won’t box in Saudi Arabia and aiming to win a world title in the next year

“I give my hidings and I take my hidings and so they have seen me with snapped ligaments in my knee, broken feet, broken toes, broken hands, stitches, broken legs,” Molly McCann says of the damage she has endured as a fighter and the impact it has had on her mum and her partner, Fran Parman. “It’s traumatic for Fran and even more traumatic for my mum. I’m 35 and I’ve been in the gym since I was 12. I had my first fight at 16. I’ve spent most of my life fighting.”

McCann boxed as a teenager and she won an ABA title. But, at a time when women’s boxing was still undermined, she turned to mixed martial arts and eventually became the most successful female British fighter in the UFC. McCann retired in March after 14 savage UFC bouts; but, within days, she became a professional boxer. On Saturday night she will have her second contest in boxing’s paid ranks.

It’s hard to disagree with Ian Wright when he suggests the midfielder has been subjected to a timeworn double standard

Sir Alex Ferguson was there. Bryan Robson was there. Eric Cantona was there. The manager Ole Gunnar Solskjær was there, and yet even as these four club legends sold the dream of Manchester United to a 17-year-old from the Midlands, they could sense the elusiveness, the coldness, the drop of the shoulder. The nagging suspicion that, like so many defenders Jude Bellingham would later encounter, they too were grasping at pure air.

“He had it planned out,” Solskjær would later remember. “He knew what he wanted. X amount of minutes in the first team. The most mature 17‑year‑old I’ve ever met in my life.” Though five years have passed since Bellingham turned down United for Borussia Dortmund, for me this is still the story that explains him best of all. The origin myth. This is what you all think I’m going to do. So I’m going to step that way instead.

Englishman was not an obvious candidate to lead them but Swedes pushed Nottingham Forest all the way in 1979

Early in the 1979 European Cup final, Kenny Burns misjudged a long ball and ended up lobbing it up in the air for Jan-Olov Kindvall. He, in turn, attempted to knock the dropping ball over Peter Shilton but the goalkeeper was not as close as he had perhaps anticipated and Shilton ended up catching it simply. The chance was gone and, with it, Malmö’s hopes of beating Nottingham Forest.

“I had quite a good chance to score and then they were the better team,” says Kindvall. “But maybe if we had got the first goal, maybe we had a chance. We were very good when we didn’t have the ball ourselves. We had good organisation in the defence. And Forest were very good without the ball as well. It was more difficult for us to play against a team who were more like our team. We played the English way.”

A boom in places offering petting sessions is linked to a rise in the illegal movement of exotic and endangered species, say experts

The second floor of an unassuming office building in central Bangkok is a strange place to encounter the world’s largest rodent. Yet here, inside a small enclosure with a shallow pool, three capybaras are at the disposal of dozens of paying customers – all clamouring for a selfie. As people eagerly thrust leafy snacks toward the nonchalant-looking animals, few seem to consider the underlying peculiarity: how, exactly, did this South American rodent end up more than 10,000 miles from home, in a bustling Asian metropolis?

Capybara cafes have been cropping up across the continent in recent years, driven by the animal’s growing internet fame. The semi-aquatic animals feature in more than 600,000 TikTok posts. In Bangkok, cafe customers pay 400 baht (£9.40) for a 30-minute petting session with them, along with a few meerkats and Chinese bamboo rats. Doors are open 12 hours a day, seven days a week.

The chancellor’s statement will be remembered for the many taxes it raised, rather than the big one – income tax – it did not

Rachel Reeves’s chancellorship was already balanced on a knife-edge, even before the 2025 budget. After she delivered her second budget statement, it still is. Even more than usual, Wednesday’s speech was full of significant fiscal changes, altered spending commitments and adjusted economic forecasts, most of them accidentally (and, for journalists, conveniently) released a short while in advance by the obviously misnamed Office for Budget Responsibility. Politically, however, almost nothing has changed at all.

Reeves arrived in the Treasury last year offering what she, like Keir Starmer, had promised as the Conservative years ebbed: competence, stability and, above all, a focus on economic growth. Her problem, despite her upbeat assessments, is that she has delivered none of them. Nothing about the 2025 budget guarantees any early change in that, however defiantly Reeves spoke about reversing the OBR’s reduced new growth and productivity forecasts.

Martin Kettle is a Guardian columnist

As they struggle with the cost of living, people weigh up whether Rachel Reeves’s measures will help them

• What the budget means for people on a range of incomes

• Budget calculator: find out if you are better or worse off

For Brett and Maria MacDonald, the cost of living has been biting this year, from rising mortgage payments to childcare fees. Living in London with two young children and no extended family nearby, the pair are juggling work with parenting.

Ralph Gonsalves campaigns on strong economy in bid to retain office he has held since 2001

Voters in St Vincent and the Grenadines will go to the polls on Thursday with Ralph Gonsalves seeking a record sixth consecutive term as prime minister.

The elections are expected to be a tight contest between the ruling Unity Labour party, which has been in power since 2001, and the opposition New Democratic party. In the last election, ULP won nine of 15 seats, but the NDP won the popular vote.

Vatican says ‘demanding’ six-day mission will be packed with meetings with political and religious leaders

Pope Leo will make his debut overseas trip as leader of the Catholic church on Thursday, travelling on a six-day mission of peace and unity to Turkey and Lebanon in what the Vatican said was expected to be a “demanding” schedule packed with meetings with political and religious leaders amid heightened Middle East tensions.

In Turkey, a country with a Muslim majority and home to an estimated 36,000 Catholics, the Chicago-born pontiff, who was elected in May, will first meet President Recep Tayyip Erdoğan in Ankara.

The leftist party exploded out of Spain’s anti-austerity protests in 2011 and upended Spain’s entrenched two-party system. I was instantly captivated – and for the next decade, I worked for the party. But I ended up quitting politics in disappointment. What happened?

• This article originally appeared in Equator, a new magazine of politics, culture and art

I never expected to retire in my 30s, but I suppose politics is the art of the impossible: what it promises, what it extracts. A decade at the heart of Spain’s boldest modern political experiment aged me in ways I’ve only just begun to fathom.

In May 2014, just four months after it was founded, the leftwing Spanish party Podemos (“We Can”) won five seats in the European parliament. As a recent university graduate who had been part of a local Podemos group (or círculo, as they were known) in Paris, I was hired to work for these MEPs. We arrived in Brussels as complete tyros and had to learn everything on the job. But we were motivated by the promise of doing what we used to call “real politics” – that is to say, not the internal power struggles and ideological weather patterns of the movement (which were always abundant), but the actual issues, such as gender discrimination and unemployment.

She’s the emerging star of this year’s dance show, wowing judges with her paso doble. The pundit and former footballer talks about gentleness, bullying, her love of the Lionesses and why she’s never been so happy

The qualities that made Karen Carney an unstoppable winger on the football pitch – her speed and attack, and the sheer relentlessness of both – are more of a hindrance in the ballroom, for some of the dances at least. As the emerging star of this year’s Strictly Come Dancing, she has had to learn to slow down, stand up straighter, to be softer, and it’s taken a lot of hard work. On week eight, she had just performed the American Smooth, and her pro partner Carlos Gu was tearfully describing Carney’s work ethic. Who could watch her trying to hold back her own tears, chewing on emotion like a particularly tough bit of gristle, and fail to see a woman who was giving it everything?

It was Carney’s dream to be on Strictly. The former England footballer, now TV pundit and podcaster, has just made it through week nine, performing an astonishing paso doble at the all-important Blackpool week, and something will have gone very wrong if she doesn’t reach the final. The show has been struggling this year – a man described as a Strictly “star” was reportedly arrested in October on suspicion of rape, and the announcement from its longtime hosts Tess Daly and Claudia Winkleman that this will be their final series has been destabilising. But Carney says that for her, it has been an overwhelmingly positive time. “There’s a team spirit within the cast. Behind [the scenes], the team can’t do enough for you to have the best experience.”

The minister says quick approvals can happen while protecting the environment, but my experience tells me that haste brings unintended consequences

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I got a text from a biodiversity advocate around midday on Thursday asking me: are you glad, or sad?

I wasn’t sure how to reply.

The driving force behind the continent’s standout team resembled four players in one as Arsenal put their old nemesis Bayern Munich to the sword

Shortly before the goal that left Arsenal’s supremacy in no doubt, Harry Kane embarked upon a lonely jaunt up their left flank. Much like the majority of Bayern Munich’s attacking endeavours, it ended almost as soon as it had begun. In common with a sizeable percentage it was terminated by Declan Rice, who thundered in and took the ball cleanly with a hooked right foot to a cheer that rivalled the night’s loudest.

The Emirates Stadium crowd was always going to enjoy that one, as Rice knew full well. He responded in kind with a roar and an exhortation to the gallery, perhaps to his teammates too: keep it going, crank up that volume, let’s see this thing through. Rice is the best player in Europe right now and, with that, there are standards to drive.

The rankings were changed after the UN used new criteria to give a more accurate picture of the rapid urbanisation driving the growth of megacities

Jakarta has overtaken Tokyo as the world’s most populous city, according to a UN study that uses new criteria to give a more accurate picture of the rapid urbanisation driving the growth of megacities.

The Indonesian capital is home to 42 million people, according to an estimate by the population division of the UN Department of Economic and Social Affairs in its World Urbanisation Prospects 2025 report published this month.