Prince Andrew hit the headlines in January after being named in court papers in the US.
A woman alleged that financier Jeffrey Epstein, a former friend of Prince Andrew, forced her to have sex with the prince on three occasions as a young woman.
Buckingham Palace has issued two statements to "emphatically" deny the claims made about the royal.
In April, the details regarding Prince Andrew were officially struck from the court records after a judge ruled they were unnecessary to the civil case in which they were raised.
What is the legal background to the case?
Prince Andrew was not party to the proceedings. Instead he was named in papers, filed in a motion in a Florida court, as part of evidence relating to a wider case involving Epstein.
Two women, known as Jane Doe #1 and Jane Doe #2 - the name used in US legal proceedings for people with anonymity - are suing the US government.
They claim the government failed to protect their rights when it entered into a plea deal with Epstein - who spent time in jail in 2008-9 for a sex offence with a minor.
Two more women, Jane Doe #3 and Jane Doe #4, wanted to join the case. It is the woman known as Jane Doe #3 who has made claims against Prince Andrew.
The court document alleges Epstein sexually trafficked the woman, making her available for sex to "politically connected and financially powerful people".
In the court papers, Jane Doe #3 said she had been forced to have sexual relations with the duke in three locations - in London, New York and on a private Caribbean island owned by Epstein - between 1999 and 2002.
She has been named in reports as Virginia Roberts.
At the time the documents emerged, Ms Roberts issued a statement through her lawyers, saying she was "looking forward to vindicating my rights as an innocent victim and pursuing all available recourse". She said she was not going to be "bullied back into silence".
Who is Prince Andrew?
The prince, 54 and fifth in line to the throne, stepped down as UK trade envoy in July 2011 following controversy over his friendship with Epstein.
The prince had visited Epstein in December 2010 after the tycoon served part of an 18-month prison sentence for soliciting a minor for prostitution. The pair had also met at Epstein's Florida home over the years. Prince Andrew later acknowledged his friendship with Epstein had been a mistake.
The prince carries out official engagements on behalf of the Queen, focusing on the areas of education and skills, entrepreneurship, and science, technology and engineering.
He has two daughters, Beatrice and Eugenie, with former wife Sarah Ferguson.
What has Buckingham Palace said?
When the allegations surfaced in January, the palace said it would not comment in detail on the legal proceedings but released two statements.
In the first, a Buckingham Palace spokeswoman said: "This relates to long-standing and ongoing civil proceedings in the United States, to which the Duke of York is not a party.
"As such we would not comment on the detail. However, for the avoidance of doubt, any suggestion of impropriety with under-age minors is categorically untrue".
A second statement issued two days later, after further details about allegations were published in Sunday newspapers, stressed that claims made about the duke were "without any foundation".
In it, Buckingham Palace said: "It is emphatically denied that the Duke of York had any form of sexual contact or relationship with Virginia Roberts."
Prince Andrew spoke about the claims at a World Economic Forum reception in Davos, Switzerland.
He said: "I just wish to reiterate and to reaffirm the statements that have already been made on my behalf by Buckingham Palace. My focus is on my work."
Who else was involved in the case?
US lawyer Alan Dershowitz was also named in the court documents as one of three men alleged to have had sexual relations with the woman.
He said he was planning legal action against the woman. He has also said that Prince Andrew should take legal action himself.
Mr Dershowitz has said of the case: "You cannot allow these false allegations simply to remain out there, and you cannot allow people who make false allegations to have the freedom to continue to make them."
Ghislaine Maxwell, daughter of late newspaper tycoon Robert Maxwell, has said claims against her are "obvious lies" after she was also named in the court papers. She has previously denied any wrongdoing.
Her spokesman said: "The original allegations are not new and have been fully responded to and shown to be untrue. Each time the story is retold it changes, with new salacious details about public figures and world leaders."
What is the latest?
In April, a judge ruled that the details regarding Prince Andrew be struck from the court record as they were "unnecessary" to decide the civil case.
Judge Kenneth Marra said: "The factual details regarding with whom and where the Jane Does engaged in sexual activities are immaterial and impertinent to this central claim."
Mr Dershowitz said he felt completely vindicated by the judge's ruling.
The judge also denied the application by Ms Roberts and Jane Doe #4 to join the case as plaintiffs.
Lawyers for Jane Doe #3 said they did not believe the ruling to be the end of the case for their client.