After the world waited anxiously for the birth of the royal baby, the as-yet-unnamed new prince has already been stealing the hearts of millions, having made his first royal appearance swathed in a blanket and held by his proud parents, the Duke and Duchess of Cambridge, outside of the Lindo wing where Kate Middleton gave birth on Monday.

How was Baby Cambridge's first day out of the luxurious Lindo wing and in the world, and how are the new parents feeling now?

Yesterday evening, Kate Middleton and Prince William traveled to their current home in Kensington Palace with baby in tow, the Daily Mail reports, where Pippa Middleton and James Middleton were waiting eagerly to meet her nephew. It is unclear whether or not excited uncle Prince Harry has met the royal baby yet, as he raced back from Wattisham airbase in Suffolk last night, where he is currently stationed on duty with the RAF.

This morning, the royal baby was visited by Her Majesty, as the Queen has delayed her travel plans until Friday to meet him. The Daily Mail suspects that the potential name of the new prince was discussed during the visit.

Last night, the Queen told Buckingham Palace guests that she was "thrilled" at the birth of her great-grandson. She infamously told a 10-year old schoolgirl on the eve of the baby's birth that the gender of the child did not matter to her, adding, "I would very much like it to arrive. I'm going on holiday."

The Duke and Duchess looked happy and fresh-faced this afternoon, escorted by security while in their private car while driving to a location that palace officials would not confirm. However, their black Land Rover was spotted arriving at the home of grandparents Carole and Michael Middleton's home in Bucklebury, Berkshire, where the Duchess spent the last few days of her pregnancy keeping cool from the summer heat. Additional security has been provided for the Middleton mansion in preparation for the royal couple's visit.

It is not possible to tell whether the Duchess's siblings, Pippa and James, were at the 18-acre estate today along with their parents.

Yesterday, Prince William told an ecstatic crowd outside of the Lindo wing that they were "still working on a name" for their son, reportedly because the Duchess wanted to see her son's face "little face" and get to know him before choosing one.

"He's a big boy, quite heavy. We're still working on a name," Prince William told reporters, adding: "Well he has a good pair of lungs on him, that's for sure."

When asked jokingly about the baby's "lateness", as the prince took longer than expected to arrive, Prince William said, "I will remind him of his tardiness when he is older," adding with a grin, "He's got her looks thankfully," to which the Duchess responded, "No, no, no I'm not sure about that."

The baby was born 8lbs 6oz, and the Duchess and new mother said, "It's been very emotional. Any parent will know what this feeling is like."

After their first public appearance, the royal parents safely strapped their son into his carseat, a daunting task for any new parent, let alone for one being watched by the entire world. The crowd cheered as the royal couple was escorted to their home. By October at the latest when renovations are finished, it is hoped the royal couple will move into their new residence, Apartment 1A at Kensington Palace, where the baby's luxurious nursery awaits him.

After her husband's two weeks on paternity leave, the Duchess plans to spend six weeks with her baby at her parent's home in Berkshire while the Duke completes his present tour of duty with the RAF in Anglesey, North Wales.

Last night, bookies placed their bets on George and James, the current most popular choice monikers for the new prince, with hundreds of thousands of possibilities at stake. Alexander, Henry, Louis, Richard and Arthur were the next most popular picks.

While in their car leaving Kensington Palace this afternoon, the Duke and Duchess waved and smiled at onlookers of their new family, chatting to their newborn in his carseat, the Duchess's hand resting near her baby.

Click here to see photos of the Duke and Duchess with their baby on the prince's first day out, as well as pictures from their first appearance outside of the Lindo wing.