How will the ruling affect businesses?
One of the areas where today's ruling will no doubt have a large impact is on businesses, where employers must ensure employees feel represented and safe at work.
Philip Pepper, employment partner at law firm Shakespeare Martineau, said the ruling will offer long-term clarity for businesses.
He urged for the Equality Act 2010 to be "urgently" updated to prevent any "potential inequality of treatment" that may occur as a result of the judgment.
"Whilst that process is ongoing, employers should take extra care to ensure that transgender employees feel safe, represented and valued in the workplace," he said.
"Employers may have to rethink their policy towards single-sex spaces in the workplace, such as bathrooms and changing rooms, and ensure that all individuals have a suitable space that they feel comfortable in when needing to use those facilities.
"Some workplaces have become divided on the issue, which means communication, training and zero tolerance on bullying will be vital to ensure that transgender employees do not feel uncomfortable at work.
"While this decision will be disappointing for some, it ultimately offers a clear path forward for employers who can now ensure they stay on the right side of law."
JK Rowling reacts to Supreme Court ruling
JK Rowling has just shared her response to today's Supreme Court ruling.
The Harry Potter author is a supporter of For Women Scotland, the campaign group which took on the Scottish government in the case.
A 'really wounding' ruling
We've just had some reaction to today's ruling from diversity, equity and inclusion expert Hannah Ford.
She tells presenter Gareth Barlow that the Supreme Court's decision could be "really wounding" for the trans community and an uphill battle remains for employers ensuring their workplaces can be a safe space.
"They will very much see this judgement is wounding them and will be viewed as anti protectionist," she says.
"Many employees on the ground say that their real life experience is that they were underrepresented and that they're made to feel not part of the workforce."
However, Ford adds that many employers will benefit from the clarity of today's ruling.
"If we can take one positive from today's judgement, it's that in this finding that sex means biological sex and woman means biological woman, at least we have simplicity and clarity.
"So it is in one sense a triumph of sense over legal coherency."
Sturgeon owes me an apology, former SNP MP says
Joanna Cherry, the former SNP MP and women's rights campaigner, says Nicola Sturgeon owes her an apology for criticising her support for “the rights of women and lesbians”.
"I'm a long-term feminist," she said. "I'm a lesbian who came out in the '80s and campaigned against Section 28.
"I've had to put up with my own party leader, Nicola Sturgeon, calling me a bigot and a transphobe for sticking up for the rights of women and lesbians.
"I think she owes all of us, not just me, and more importantly the women of Scotland, an apology."
Cherry, who lost her seat in last year's general election, also urged Scottish First Minister John Swinney and Sir Keir Starmer to "respect this judgement" and protect women's rights, as well as single-sex spaces.
Supreme Court ruling 'incredibly worrying', Stonewall says
Leading LGBTQ+ charity Stonewall has issued a statement on today's Supreme Court ruling, calling it "incredibly worrying" for the trans community.
"Stonewall shares the deep concern at the widespread implications for today's ruling from the Supreme Court," Simon Blake, Stonewall CEO, says.
"It will be incredibly worrying for the trans community and all of us who support them. It’s important to be reminded the court strongly and clearly re-affirmed the Equality Act protects all trans people against discrimination, based on Gender Reassignment, and will continue to do so.
"Once we read and fully digest the judgement, we will work with stakeholders across all sectors to provide as much clarity as possible.
"Stonewall will continue its work with the Government and parliamentarians to achieve equal rights under the law for LGBTQ+ people."
John Swinney: Protecting rights of all will underpin our actions
We've just had a statement from John Swinney, the Scottish first minister - as you know, the ruling this morning was in the case For Women Scotland v The Scottish Ministers and was the culmination of a years-long fight between the Scottish government and campaigners.
Posting on X, Swinney says the Scottish government accepts the judgment...
Watch: Women break into song after ruling
Here's the moment that women in Edinburgh broke out into song after the Supreme Court's ruling this morning.
Our Scotland correspondent Connor Gillies was there to witness it...
'Victory for common sense' - politicians react
We've heard from the UK government - here's the reaction from other politicians, including Kemi Badenoch.
The Tory leader lauded the "victory" at court, adding: "Saying 'trans women are women' was never true in fact, and now isn't true in law either.
"This is a victory for all of the women who faced personal abuse or lost their jobs for stating the obvious. Women are women and men are men: you cannot change your biological sex.
"The era of Keir Starmer telling us women can have penises has come to an end."
'Apology letters'
Rosie Duffield, a former Labour MP and outspoken supporter of For Women Scotland, the campaign group that brought the case, posted on social media: "We're all going to need industrial-sized postboxes to accommodate all the grovelling apology letters - biggest one for all the women in Scotland who were never ever going to weesht!"
Weesht is a term used in Scotland meaning "hush" - or "whisht".
In a separate statement, she said she was "just thrilled and relieved".
'Government must clarify guidance'
Mims Davies, the shadow minister for women, shared a "well done" message for For Women Scotland, but added the government must clarify guidance to reflect the Supreme Court's ruling.
"This morning's decision is important for women right across our country," she added.
"This is a clear victory for common sense - and should never have taken a court case to prove the biological definition of a woman."
Tears of joy at court despite judge warning there is no 'triumph'
By Sarah Hajibagheri, at the Supreme Court
Loud applause erupted in court, followed by tears of joy and warm embraces among the For Women in Scotland campaigners as the judges left the room.
The outpouring of emotion, group hugs, cheers and tear-stained smiles were in stark contrast to the austere portraits of men in uniform that adorn the dark wood panelled Court 1 of the Supreme Court.
The packed room had been warned at the start of proceedings that, despite the "strength of feeling on all sides", everyone was to respectfully listen to proceedings as "some people will be pleased, others will be disappointed" by what was to be said.
Everyone complied.
But there was an audible collective inhale of breath by those gathered inside when Lord Hodge announced the "unanimous decision" that "woman" and "sex" in the Equality Act 2010 referred to "a biological woman".
He cautioned against "seeing this as a victory for one side or the other" but the beaming faces of the women sat below the stained-glass windows at court suggested they felt vindicated.
Seats on the carved wooden pews were ticketed and highly sought.
The media benches were full, but no laptops were allowed inside and those that didn't make it in were in an overspill room.
In a nuanced hand down, Lord Hodge said: "We counsel against reading this judgement as a triumph of one or more groups in our society at the expense of another. It is not."
But as those inside Court 1 spilled out to meet with fellow supporters - the cheering and singing began.
Their appeal had been successful, and this was being celebrated as a win for them.
JK Rowling among famous backers of campaign that took Scottish ministers to court
For Women Scotland has been backed by a number of famous campaigners, including bestselling author JK Rowling.
The Harry Potter writer has been at the centre of transphobia accusations for years and faced considerable backlash for her comments, including from cast members of both the Harry Potter and Fantastic Beasts film franchises.
In 2020, Rowling shared an essay on her website on sex and gender issues, which included speaking out on the "five reasons for being worried about the new trans activism".
The essay explained that her views on women's rights sprang from her experience of domestic abuse and sexual assault.
Other FWS supporters include Graham Lineham, creator of The IT Crowd and Father Ted, who was present at the ruling in London this morning.