In the UK, marches took place in Edinburgh, London, Cardiff, Bristol and other cities. Smaller events were held in places including Lerwick, in Shetland, and the Isle of Eigg.
But the biggest protests were held in the US, where more than 500,000 people gathered for a rally outside the US Capitol building in Washington DC. Other protest rallies took place in New York, Chicago and Los Angeles as Americans woke up to the first day of a Trump presidency.
Celebrities Katy Perry, Scarlett Johansson, Amy Schumer and Patricia Arquette were among the demonstrators at the Washington event.
Ugly Betty star America Ferrera, who helped organise the march, told the crowd: “It’s been a heartbreaking time to be both a woman and immigrant in this country.
“But the president is not America. His cabinet is not America. Congress is not America. We are America and we are here to stay.”
Hillary Clinton tweeted her support to the marchers, thanking them for “standing, speaking and marching for our values”.
Desperate Housewives star Felicity Huffman also joined the march. She said: “The best of us was bested by not the best of them.”
Many of the women in Washington wore pink knitted hats with cat ears – a reference to comments made by Trump in a 2005 leaked video in which he bragged about grabbing women “by the pussy”.
Protesters carried signs with anti-Trump slogans including “Not my president” and “Predator in chief”.
Beginning at the American Embassy in London, the London Women’s March made its way around the streets of the capital and to a rally in Trafalgar Square. An estimated 100,000 people took part.
The movement states on its website that the US election “proved a catalyst for a grassroots movement of women to assert the positive values that the politics of fear denies”.
Organisers called for people to join them “as part of an international day of action in solidarity” on President Trump’s first full day in the Oval Office.
People across all ages and genders descended on Grosvenor Square holding a rainbow of placards with slogans such as “Dump Trump”, “Reject hate, reclaim politics” and “No to racism, no to Trump”.
Labour MP Harriet Harman was joined on the march by friend and American-British playwright Bonnie Greer.
Referring to outgoing US president Barack Obama, Harman said: “It’s just a shame they have a two-term limit, isn’t it?”
Greer warned that Trump’s presidency was “not a joke”, adding: “This is for real and I think this march demonstrates that London understands that.”
Labour MP Yvette Cooper, who spoke at the rally, said: “When the most powerful man in the world says it’s OK to sexually assault women because you are rich and powerful, we have to stand up and say no way.”
She added: “I think this is a march for equality and action for the future. We don’t want the clock being turned back on women’s equality.”
In Germany one protester held up a sign which read: “Mr Trump, you are no Berliner.”
At least 2,000 people gathered outside the US consulate in Edinburgh to show their opposition to President Trump.
The protesters, mainly women, object to the alleged sexism, racism and homophobia of the newly inaugurated US leader.
One of the organisers of the Scottish event, Leah Higgins from Lanarkshire, said it was important to show people in America who were worried by the Trump presidency they were not alone.
She said: “I organised this to show solidarity with our sisters and brothers in the US.
“There’s many of these (events) going on all over the world and I felt Scotland should have one as well.
“It’s been overwhelming. We’ve had so much support. I’m just really happy that so many people have turned up.”