The Duke of Edinburgh's coffin has been carried to St George's Chapel, with members of the Royal Family walking behind his coffin.
His children Princess Anne and Prince Charles made up the front row, followed by Prince Edward and Prince Andrew.
In the third row, Prince William and Prince Harry walked either side of their cousin Peter Phillips.
The service, which is being broadcast on BBC One, will start after a national minute's silence at 15:00 BST.
The ceremonial royal funeral will remember Prince Philip's "unwavering loyalty" to the Queen, service to the nation and "courage".
The duke's association with the Royal Navy and love of the sea will also be a focus but no sermon will be delivered, in line with his wishes.
More than 730 members of the armed forces are taking part in the event, but there is a limit of 30 mourners at St George's Chapel, under Covid rules.
Representatives from military units with a special relationship to the duke are positioned in the castle's Quadrangle, with music provided by the Band of Royal Marines Commando Training Centre, the Band of the Scots Guards and the Combined Bands of the Royal Air Force.
Prince Philip died at Windsor Castle on Friday 9 April, aged 99.
His coffin was carried the short distance to St George's Chapel on a modified Land Rover, which the duke himself helped to design.
The funeral procession from the castle to the chapel was headed by the Band of the Grenadier Guards, the Major General's party, and military service chiefs.
Vice Admiral Sir Timothy Laurence and the Earl of Snowdon also walked behind the coffin, trailed by members of the duke's household staff.
The Queen, 94, travelled with a lady-in-waiting in the state Bentley at the end of the procession.
Following the procession, a Royal Marines bearer party carried the coffin into the service.
And buglers of the Royal Marines will sound Action Stations - a signal that all hands should be ready for battle - as the coffin is lowered into the Royal Vault at the end of the service.
A reduced choir of four singers will feature but the congregation will follow Covid restrictions and not sing.
A ceremonial gun fire at nine locations across the UK, and in Gibraltar, is marking the start and end of the national minute's silence.
Heathrow Airport said no planes would land or take off for six minutes to coincide with the silence and all major sporting events have been rescheduled to avoid a clash with the funeral.
The funeral service will be conducted by the Dean of Windsor, with the Archbishop of Canterbury pronouncing the blessing.
The Order of Service, released by Buckingham Palace, says the Dean of Windsor will pay tribute to Prince Philip's "kindness, humour and humanity" and the "many ways in which his long life has been a blessing to us".
"We have been inspired by his unwavering loyalty to our Queen, by his service to the nation and the Commonwealth, by his courage, fortitude and faith," he will say during his bidding.
image copyrightPA Mediaimage captionThe duke's insignia is displayed on the altar in St George's Chapel
Buckingham Palace said the funeral plans had been modified to take into account public health guidelines.
The funeral will take place entirely within the grounds of the castle and the public have been asked not to gather there or at other royal residences.
The congregation will put on masks and socially distance in line with Covid lockdown rules, with the Queen seated alone.
But the ceremonial aspects of the day and the service remain in line with Prince Philip's wishes and will reflect his military affiliations and personal elements of his life.
The music will include the 1860 hymn Eternal Father, Strong to Save, by William Whiting, which is associated with seafarers and the maritime armed services.
Ahead of the funeral, the Queen shared a favourite photograph of herself with the Duke of Edinburgh, showing the couple in Aberdeenshire.
Taken by the Countess of Wessex in 2003, the picture shows the couple relaxing on a picnic rug on the grass at the Coyles of Muick beauty spot, near the Queen's private estate of Balmoral.
image copyrightThe Countess of Wesseximage captionThe Queen released one her favourite photos ahead of the funeral
The 30 guests at the funeral wore morning coats with medals, or day dress, but not military uniform.
The Queen and duke's four children - the Prince of Wales, the Princess Royal, the Duke of York and the Earl of Wessex and - as well as their eight grandchildren - are attending, but none of their young great-grandchildren.
Spouses of the children and grandchildren joined the congregation, including two who have married into the family in recent years - Jack Brooksbank and Edoardo Mapelli Mozzi, husbands of Princesses Eugenie and Beatrice.
But the Duke of Sussex's wife, Meghan, is heavily pregnant and was advised by her doctors not to fly in from the US.
The other mourners include the children of the Queen's sister, Princess Margaret, and three of Prince Philip's German relatives - Bernhard, the Hereditary Prince of Baden; Donatus, Prince and Landgrave of Hesse; and Prince Philipp of Hohenlohe-Langenburg.
image copyrightGetty Imagesimage captionThe Foot Guards Band were seen marching outside Windsor Castle ahead of the procession
Meanwhile, poet laureate Simon Armitage has published a poem to mark the death of Prince Philip, paying tribute to the duke's generation as the "last of the great avuncular magicians" who "kept their best tricks for the grand finale".
How to follow the funeral on the BBC
Can I watch the funeral on TV?
Live online coverage of the procession and funeral is available on the BBC News website and app, and the service will be streamed in the UK and internationally.
Television coverage in the UK is under way on BBC One, the BBC News Channel and on BBC iPlayer.
On the radio, you can follow the day's events between 14:00 BST and 16:10 BST on Radio 4 and Radio 5 Live, and simulcast on BBC World Service English, BBC Radio Scotland, and BBC Radio Ulster.
BBC Radio Wales and BBC local radio will also cover the event, with start times to be confirmed.