• Nomadland's Chloe Zhao made history as the first woman of colour and second woman to win best director.
• Sir Anthony won the best actor for his masterful performance as a man suffering from dementia in The Father, 29 years after he won his first Oscar for The Silence of the Lambs.
Film drama Nomadland has scooped three Oscars including best picture, while British stars Sir Anthony Hopkins and Daniel Kaluuya have won acting awards.
Nomadland's Chloe Zhao made history as the first woman of colour and second woman to win best director.
Sir Anthony, 83, is the oldest winner of best actor, while Kaluuya is the first black British actor to win an Oscar - for the best supporting award.
British actress-turned-writer/director Emerald Fennell won a screenplay award.
She won best original screenplay for Promising Young Woman, which she also directed.
Frances McDormand won best actress for her role in Nomadland, while veteran South Korean actress Yuh-Jung Youn won best supporting actress for Minari.
The trophies were handed out in one of the grand halls at Los Angeles's stylish Union Station to allow for a Covid-safe ceremony, while many UK-based nominees were at a venue in London - although Sir Anthony was at neither.
Absent Sir Anthony beats Boseman
Sir Anthony won the best actor for his masterful performance as a man suffering from dementia in The Father, 29 years after he won his first Oscar for The Silence of the Lambs.
His victory was the biggest surprise of the night. The award had been tipped to go to the late Chadwick Boseman, who died at the age of 43 last August, for Ma Rainey's Black Bottom.
It was perhaps a surprise to Sir Anthony himself, who was neither in LA nor at the British Film Institute in London, the ceremony's UK venue.
The actor was thought to be in his native Wales, and there was not an option to appear via Zoom, meaning he did not appear on screen or in person.
The Father also won best-adapted screenplay for Sir Christopher Hampton and Florian Zeller, who called Sir Anthony "the greatest living actor".
Big night for Nomadland
The slow-burning drama about a woman living in her van in the American West after the financial crash won the top prize for best film, plus best director and best actress.
McDormand, who now has three best actress Oscars, is one of the only professional performers in the film. Most of the rest of the cast is made up of real people playing fictionalised versions of themselves.
In her acceptance speech, Zhao thanked the real-life nomads "for teaching us the power of resilience and hope".
Before Zhao, the only woman to have won the directing prize in the Oscars' 92-year history was Kathryn Bigelow for The Hurt Locker in 2010.
McDormand spoke of her hopes for the revival of big-screen cinema, asking viewers: "One day very, very soon, take everyone you know into a theatre, shoulder to shoulder in that dark space and watch every film that's represented here tonight."
She then said: "We give this one to our Wolf," and howled like a wolf - a tribute to the film's sound mixer Michael Wolf Snyder, who took his own life at the age of 35 last month.
Meanwhile, black-and-white film Mank, which led the nominations with 10, picked up two awards, as did Sound of Metal, Judas and the Black Messiah, Ma Rainey's Black Bottom and Soul.
The big winners
- Nomadland - 3
- The Father - 2
- Judas and the Black Messiah - 2
- Ma Rainey's Black Bottom - 2
- Mank - 2
- Soul - 2
- Sound of Metal - 2
- The winners and nominations in full
Victorious Kaluuya 'happy to be alive'
The 32-year-old Londoner won best-supporting actor for his incendiary performance as Black Panthers leader Fred Hampton in Judas and the Black Messiah.
"What a man. How blessed we are that we live in a lifetime where he existed," the actor said. "I am humbled to be nominated for portraying a man whose principles I deeply respect and for guiding me to walk in his footsteps."
Kaluuya also paid tribute to his mother, who was watching at the BFI, who he said "gave me my factory settings so I can stand at my fullest height".
But she could be seen asking "What is he talking about?" when her excited son told the global audience of millions: "My mum met my dad, they had sex, it's amazing. I'm here. I'm so happy to be alive so I'm going to celebrate that tonight."
Yuh-Jung Youn became the first South Korean actress to win an Oscar, for her role as the grandmother in Korean-American family drama Minari.
She beat Olivia Colman, Amanda Seyfried, Maria Bakalova and Glenn Close to the prize for best supporting actress. It was Close's eighth nomination without a win. Youn told the crowd she "doesn't believe in competition" and paid tribute to her fellow nominee, asking: "How can I win over Glenn Close?"
Ugandans online have cheered on British actor Daniel Kaluuya who is of Ugandan origin after he won an Oscar.
In his speech he thanked all his fans from London and Kampala.
His Ugandan mother who was in the audience was also credited for her contribution in his career.