- Everything we know so far after Duchess gives birth to boy
- New Prince of Cambridge receives family visitors at home
- Prince Charles jokes: I don't know how I'm going to keep up
- Gun salutes fired in London to celebrate new Royal baby
- Arthur... Albert... Philip? Latest Royal baby name odds
- Proud father and besotted mother introduce newborn to world
- 'Cutie the third': How the world reacted to prince's birth
- Royal family tree updated: Line of succession to throne changed
The Duke and Duchess of Cambridge have begun introducing their new prince to family members, as the world awaits an announcement on the baby's name.
Prince William and Kate have retreated to the sanctuary of Kensington Palace after showing off their third child to the world on the steps of the Lindo Wing.
As the Duke and Duchess settle into life as a family of five, the first visitors began arriving at their west London home on Tuesday. Pippa Middleton, the Duchess's sister, was the first to be pictured after meeting the as-yet-unnamed baby.
Video: Auntie Pippa meets baby - Duchess's sister leaves palace
Prince Harry and Meghan Markle could have been the first to visit as they are neighbours at Kensington Palace. The new baby prince's great-grandmother the Queen, 92, is still at Windsor Castle with the Duke of Edinburgh who is recuperating after a hip operation.
Prince Charles said in a statement on Tuesday afternoon that he and Camilla, the Duchess of Cornwall, are "both so pleased at the news". He added: "It is a great joy to have another grandchild, the only trouble is I don’t know how I am going to keep up with them."
The name of the baby Prince of Cambridge, who was born on Monday at 11.01am weighing 8lb 7oz, has yet to be unveiled. Royals traditionally keep the public guessing before revealing their choice and William and Kate will want to share the name with the Queen and the rest of their family before making it public.
Kensington Palace said the name would be announced in "due course" but the favourite at the bookies is currently Arthur, followed by James, Philip and Albert.
The Duke fuelled speculation about the name of his new baby boy, telling a man who suggested he could suit Prince Alexander: "Funny you should say that..."
William, who left his two-day-old son with the Duchess to attend a commemoration service, teased attendees about the as-yet-unknown name, as the world waited to hear what the Prince would be called.
Told by Alexander Downer, the Australian High Commissioner, that he favoured his own Christian name as a frontrunner for the Prince, the Duke replied: "Funny you should say that... It's a good name."
The Dean of Westminster, introducing the Duke to Mr Downer's New Zealand counterpart Sir Jerry Mateparae, joked: "And Jerry would like it to be Jerry".
"It's a strong name, I have to say," the Duke conceded smiling, speaking publicly for the first time since he took his new addition home from hospital.
The Duke joined his brother Prince Harry and soon-to-be sister-in-law Meghan Markle at Westminster Abbey for an Anzac Day service, but the topic of conversation quickly turned to the new Prince.
Asked how the Duchess and the baby were doing, Prince William said: "They're very well thanks."
The now father-of-three said they are "in good form, luckily", and added: "Sleeping's going reasonably well so far, so he's behaving himself which is good news."
While the Duke's words stoked further speculation about the possibility of a Prince Alexander, the name is not likely to be a final contender as it is one of Prince George's middle names.
Video: New Prince of Cambridge's first public outing
Born fifth in line, the baby is the Queen and Philip's sixth great-grandchild and Kensington Palace said the couple, along with the Prince of Wales, the Duchess of Cornwall, Prince Harry, and the Middletons, were delighted with the news of the new arrival.
George and Charlotte, who visited their new sibling at St Mary's Hospital in Paddington, London, on Monday afternoon, are likely to be at school and nursery on Tuesday.
At 2pm on Tuesday, gun salutes were fired in London by the King's Troop Royal Horse Artillery in Hyde Park and the Honourable Artillery Company at the Tower of London to mark the birth.
Floral dress worn by Princess Charlotte on Monday sells out online
The floral smocked dress worn by Princess Charlotte as she went to meet her new baby brother has sold out online.
Confident Charlotte, who is just days away from her third birthday, was at ease in front of the world's media at the Lindo Wing in London.
She charmed the crowds on Monday, by turning to wave as she led her father the Duke of Cambridge up the steps to the hospital to meet the newborn baby prince.
Her blue Periwinkle dress, with Peter Pan collar and short sleeves, and blue daisy smocking was by Little Alice London.
The outfit, which is priced from £40 for aged six months to £45 for six years, has sold out in all sizes.
The dress features contrast piping on the collar and sleeves, and a button back and sash tie.
The brand, which specialises in smocked clothes, is owned by Alice Avenel - who went to school at Marlborough College with Charlotte's mother the Duchess of Cambridge.
Young Pc tells of 'highlight of my career' as he appears in background of Royal baby photos
A young Metropolitan Police constable, Tyler O'Hare, took centre of stage during the Royal baby's first public appearance. Sort of...
He was in the background of many of the pictures outside the Lindo Wing as the "door officer" when the Duke and Duchess of Cambridge stepped outside with the new prince.
Pc O'Hare posted pictures on Twitter, saying it was "an honour and utter privilege". He added: "Today was an amazing day and a highlight of my career!"
The Royal couple introduced two new members to the family today....— PC Tyler O'Hare (@TylerOHare) April 23, 2018
An honour and utter privilege to have been the ‘Door Officer’ for the birth of Their Royal Highnesses new baby boy! Today was an amazing day and a highlight of my career! #RoyalBaby3#RoyalBaby3#RoyalBabypic.twitter.com/md6kMw3WSs
New father Prince William pictured leaving palace
The Duke of Cambridge has been spotted leaving Kensington Palace this afternoon. Prince William was pictured driving himself away from the family home. It's unclear where he was going - perhaps popping out for some essential supplies?
Historian Hugo Vickers on why the Royal baby's name might not matter as much as you think
Hugo Vickers, the Royal biographer and historian, explains in this video the meaning behind the most popular possible name choices for the latest baby Cambridge - and why the choice might not matter as much as you think.
Countess of Wessex 'thrilled' for Cambridge family
During a visit to Tregolls School in Truro, Cornwall, the Countess of Wessex said she did not know the name of the latest addition to the Royal family.
She said: “The jury’s out on that one. I don’t know, we’re all just going to have to wait and see.
“I’m thrilled for them all, it’s lovely - really good news.”
Video: Moment royal birth was marked by 41 round gun salute
Gun salutes mark Royal birth
Gun salutes have been fired in London by the King's Troop Royal Horse Artillery and the Honourable Artillery Company to mark the birth of the Duke and Duchess of Cambridge's baby boy.
The soldiers, horses and Guns of The King's Troop Royal Horse Artillery rode out from Wellington Barracks into Hyde Park for a 41 round salute.
And the Honourable Artillery Company (HAC), the City of London's Army Reserve regiment, fired a 62-round Gun Salute from The Tower of London.
Punters back James and Henry... but Arthur remains bookies' favourite
Punters have been racing to place bets on the possible name of the royal baby boy, with James and Henry catching favourite Arthur.
Bookies still have the moniker of the legendary king as their top name, but are seeing Royal fans taking a punt on other choices facing the Duke and Duchess of Cambridge.
William Hill spokesman Rupert Adams said: "Henry has been very popular overnight and might well be in the frame."
The firm has Arthur as 2-1 favourite, but the odds on Henry have been shortened from 14-1 to 10-1.
Other popular names include James 4/1, Phillip 5/1 and Albert 6/1.
Coral spokesman Harry Aitkenhead said: "Arthur is the hot favourite at the moment and ever since the birth yesterday our customers have been queuing up to get their bets on.
"James, Albert and Philip have also been backed and anything else would be a major shock."
He added their favourite was Arthur 2-1, followed by James 4-1, Albert 5-1, Philip 6-1, and Alexander and Henry both with odds of 12-1.
Click here for the latest odds on possible Royal baby names - and history behind them.
Auntie Pippa meets the new prince: Kate's sister pictured leaving Kensington Palace
Pippa Middleton, the Duchess of Cambridge's sister, is the first member of the family to be spotted at Kensington Palace today.
The 34-year-old was pictured leaving the Royal couple's home after meeting the as-yet-unnamed baby for the first time.
Westminster Abbey bells ring out to celebrate Royal birth
The birth of the Duke and Duchess of Cambridge's baby boy has been marked by bell ringing at Westminster Abbey.
Bell-ringers ring a peal from 1pm to celebrate the prince's arrival.
Prince Charles: I don’t know how I am going to keep up with grandchildren
The Prince of Wales said he and Camilla, the Duchess of Cornwall, are "both so pleased at the news".
Prince Charles said in a statement: "It is a great joy to have another grandchild, the only trouble is I don’t know how I am going to keep up with them.”
Royal Collection releases official souvenirs before baby even has a name
The official commemorative souvenirs marking the birth of the Duke and Duchess of Cambridge's baby son have gone on sale - before the new prince's name has been announced.
Featuring a lion cub and unicorn inspired by the Royal Arms, the Royal Collection china is decorated with gold ribbons, silver pompoms and a coronet-inspired pattern.
The pieces bear the words "Welcome to our new royal baby" and display William and Kate's coronet.
The official range includes a pillbox costing £35, a tankard for £39 and a plate priced at £49.
Each item in the range is gilded with 22-carat gold and made in Stoke-on-Trent using traditional methods.
There is also a pram-shaped woven decoration, made with glistening threads, delicate pearl detail, and embroidered on the back with "Royal Baby 2018", for £14.95.
Royal history of Arthur... and other names new prince could be given
A middle name of the Prince of Wales, Arthur is also one of Prince William's middle names as well as the Queen's father, George VI.
The legendary King Arthur was the mythical leader of the knights of the Round Table, who supposedly lived in the 5th or 6th century.
Once popular, the name fell out of fashion, but has had a revival in recent years. Former prime minister David Cameron has a son called Arthur.
Queen Victoria used to insist that the name Albert was used as a middle name by her descendants, if not a first, in honour of her much-loved consort Prince Albert.
By choosing Albert or Bertie for a boy, the Duke and Duchess would be honouring Queen Elizabeth II's father, George VI, who was actually Albert Frederick Arthur George but always known to his family as Bertie.
Shy, stammering Bertie was forced to become king when his brother Edward VIII abdicated, but won the nation's affection by standing firm in London during the Second World War.
A lasting tribute to the Duke of Edinburgh might see the new Prince of Cambridge called Philip.
Both Prince Charles and Prince William have Philip as a middle name.
The Duke of Edinburgh - known for his dedication to duty and his acerbic wit - has been married to the Queen for more than 70 years and is the nation's longest serving consort.
A Prince Freddie of Cambridge would have a historical link to the 1st Duke of Cambridge.
Prince Adolphus Frederick lived from 1774 to 1850 and was a son of George III.
He was apparently very fond of interrupting church services by bellowing out "By all means" if the priest said "Let us pray".
William may want to pay tribute to his father - but perhaps as a middle name as it may be considered too similar to Charlotte.
James could be chosen to signify the Duchess's affection for her brother, the baby's uncle, James Middleton.
William already has a cousin James, the Earl and Countess of Wessex's son, Viscount Severn.
James is a Stuart name. James I, son of Mary, Queen of Scots, had been king of Scotland for 36 years as James VI when he became king of England in 1603.
They could choose William as a middle name for a boy, but also perhaps Michael as a middle name out of respect for Kate's father.
Kate's grandfather on her paternal side was called Peter, while on her maternal side, her grandfather was Ronald.
Thomas also appears several times in Kate's family tree, as does Francis.
Who will be godparents to the new Baby Cambridge?
When it comes to godparents, the youngest Cambridge child might well be dealt the best hand yet. After seven years of marriage (and three children), the Duke and Duchess now know exactly who their real friends are.
Plus, with 12 godparents between them, Prince George and Princess Charlotte have already ticked off all those their parents felt obliged to ask. Admittedly a few of their oldest and best friends have already been bagged – Emilia d’Erlanger, for example, is George’s godmother and Prince William’s friend, Tom Van Straubenzee belongs to Chalotte – but there are plenty more of their friends waiting in the wings, as well as a few close cousins.
Click here for our best guestimate at who might be in the frame for possible godparents to the new prince.
Meet the Duchess of Cambridge's Royal 'glam squad'
It would be a worst nightmare for most new mothers, but the Duchess of Cambridge had a close knit team of helpers on hand to help ensure she looked her best for her moment in front of the world's media.
For the past few years, the Duchess has worked closely with former PA Natasha Archer and hairdresser Amanda Cook Tucker to ensure that her every public appearance is pristine.
The duo are often spotted loading vanity cases and suit carriers onto the royal jet during tours or lurking behind the scenes to tend to the Duchess whenever she needs.
Here is everything you need to know about the Royal "glam squad", who were on hand for the Duchess's Lindo Wing exit.
Arthur is bookies' favourite - but James most popular with punters
Arthur remains the bookmakers' favourite for the new Royal baby's name, but James is the most popular for individual wagers placed with Ladbrokes.
James has seen the largest amount of bets and money placed since the Duchess of Cambridge gave birth.
It is the same name as the Duchess of Cambridge's brother, James Middleton. Prince William also has a cousin James, Viscount Severn.
Despite being the favourite in the betting at 2/1, Arthur is left for second spot in the Top 10 list, followed by Albert (5/1), Philip (6/1) and Henry (12/1), according to Ladbrokes.
Jessica Bridge, of Ladbrokes, said: "Over 100,000 bets have placed across the UK betting industry on the baby name, and punters are eagerly awaiting the announcement from Kensington Palace to see if they will be quids in."
Latest Prince of Cambridge name odds
Top 10 names according to bets and money wagered
Royal gun salutes to mark birth of new baby
As well as an expected flurry of family visitors to Kensington Palace on Tuesday, Royal Gun Salutes will also celebrate the birth of the new Royal baby.
The King's Troop Royal Horse Artillery and The Honourable Artillery Company will each fire celebratory Royal Salutes at 2pm.
The soldiers, horses and Guns of The King's Troop Royal Horse Artillery will ride out from Wellington Barracks into Hyde Park for a 41 round salute.
And the Honourable Artillery Company (HAC), the City of London's Army Reserve regiment, will fire a 62-round Gun Salute from The Tower of London.
Royal baby name odds: Runners and riders for new Prince of Cambridge
Prince Arthur... Prince Albert... Prince Philip... or something else?
Asked on Monday evening whether or not he and his wife had decided on a name, the Duke of Cambridge said: "You'll find out soon enough."
As the bookmakers continue to take bets on the new Royal baby's name, click here to take a look at all the contenders.
What do you think the Duke and Duchess of Cambridge will call their third child? Vote in our poll below.
Baby prince's first achievement is to make history for gender equality
By welcoming a baby prince, William and Kate are following the birth pattern of the Queen and Philip's children - a son, a daughter and then another son.
The Queen and the Duke had Prince Charles, then Princess Anne, followed by, after a gap of 10 years, Prince Andrew, with a fourth child, Prince Edward, born four years later.
The prince's birth also made history for Royal gender equality - he is the first child to be born since an Act that secured girls' place in the line of succession.
Here's how the route to the British throne now looks.
Duke says couple are 'very happy' but have 'thrice the worry now'
Smiling broadly, the Duchess was dressed in a vibrant red Jenny Packham dress with a white lace collar, reminiscent of William's late mother Diana, Princess of Wales - who wore red and white outside the Lindo Wing after Prince Harry was born in 1984.
As William and Kate headed home after appearing in front of the banks of cameras with their seven-hour-old son, the Duke said they were "very happy" and "very delighted".
He joked, holding up three fingers, that he had "thrice the worry now", adding: "We didn't keep you waiting too long this time."
The Duke and Duchess thanked the hospital for their care and the public for their wishes.
Kensington Palace said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have received.
"They would also like to thank everyone for their warm wishes."