Known as the Earl and Countess of Strathearn, the Royal couple are touring the Strathearn area in the heart of Scotland.
Among the highlights of the day is a tour of a whisky distillery, giving them a chance to learn more about Scotland's national drink.
The couple will be given the chance to bottle their own Glenturret malt at the country's oldest distillery, near Crieff in Perthshire.
But they began their day with a visit to Strathearn Community Campus in Crieff, where they met representatives of local volunteer groups.
They were greeted by crowds of hundreds of excited locals, including many schoolchildren, who waved Saltires and Union flags.
Kate wore a coral and red striped coat by Scottish designer Jonathan Saunders and a dress by Goat.
The outfit was topped off with beige heels, a matching clutch bag and a celtic brooch given to her as a wedding present.
It is the couple's first joint engagement since returning from a tour of Australia and New Zealand last month.
On this occasion, however, the royals were not accompanied by their young son Prince George.
During the overseas trip Kate appeared to quash any speculation she may be expecting a second child when she told wine-makers how she was enjoying being able to drink again after giving birth to George.
The last time the couple travelled to Scotland in an official capacity was in April last year, when they accompanied the Prince of Wales to Dumfries House in East Ayrshire for the opening of an outdoor centre. They also visited Glasgow's Emirates Arena, a key venue in this summer's Commonwealth Games.
During the first engagement, the Duke chatted to the crew of Scotland's Charity Air Ambulance (SCAA).
William was also shown inside the aircraft and talked through its workings as he expressed a keen interest in the operation.
The encounter came days after reports suggested William, who stepped down as a search-and-rescue pilot with the RAF last year, is considering taking a role as an air ambulance pilot.
William reportedly told aides he is not ready to take on full-time royal engagements and plans are said to be under way for him to work with the East Anglian Air Ambulance service.
He is said to have made no mention of his future plans when he met the charity ambulance crew.
John Pritchard, 46, lead paramedic with the SCAA, said: "He never said a thing about it, but I would certainly welcome him on to the team.
"He is absolutely passionate about his flying and you can see he's a really caring person. I would imagine he would be keen to keep that going."
Mr Pritchard said the Duke was "really keen" to talk to the crew.
"He asked some really good questions about the aircraft and about what patients we attend," the paramedic said.
"About 60% of our call-outs are to trauma patients, motorcycle RTCs, to equestrian or off road cycle (accidents).
"He was really keen, he asked us some fantastic questions about aviation. It was really good engaging with him. His knowledge was superb.
"He wanted to have a quick look inside and see how it's all fitted. It's a smaller aircraft that what he's used to but he was really keen to see how we operated with a patient on board."
Mr Pritchard said William also talked about his own experiences of flying.
The crew presented William with a small teddy bear for Prince George, carrying the SCAA logo.
"We have a teddy on the aircraft. If we look after any children, they get presented with a teddy. So we presented that for Prince George," Mr Pritchard said.
SCAA trustee Alan Bell said the air ambulance has been in existence for just over a year and has already completed nearly 300 missions. Charitably funded, it costs around £1.5 million a year to run.
He said of William's visit: "He was very interested in the fact that it's the first charity ambulance in Scotland. He knew quite a lot about the air ambulance network in England and Wales."
The royal party spent around an hour at the community campus. For most of the visit, they met separate groups.
In addition to the air ambulance crew, the Duke was introduced to representatives of the Air Training Corps, the Sea Cadets, the Black Watch Army Cadets and the Boys' Brigade.
Kate spent most of her time speaking to young members of the Rainbows, Brownies, Guides, Beavers, Cubs and Scouts.
As part of her visit, she watched a demonstration by members of the Muthill scouts as they made Scottish pancakes.
Scout leader Jim Comrie, 66, of the 5th Perthshire group, said Kate sampled the pancakes on offer.
He added: "She was asking the children if they'd been camping, which they had about a month ago. They didn't get much sleep - that's what they were telling her.
"We also presented her with one of our neckerchiefs.
"She is a cub leader with one of the packs in England. She was asking about the different proficiency badges we've got and they were explaining what they were for."
The couple rounded off their first visit by jointly opening a reconstruction of a timber circle, known as the Pittentian Timber Circle, which was excavated in 2011 during the construction of the Beauly to Denny power line.
There are more than 80 timber circle sites in Scotland but few have been excavated, making it an important archaeological find.
The couple later visited MacRosty Park in Crieff to mark its redevelopment.
Hundreds of people, some dressed in kilts, and pupils from primary schools in Crieff, Auchterarder and Braco lined the park to welcome the couple.
Brass bands from Morrison's Academy and Crieff High played and youngsters waved Union and Saltire flags as William and Kate arrived.
A group of councillors, local business owners and Perthshire provost Liz Grant greeted the couple at the park's bandstand, where William unveiled a plaque which marks the park as a field in trust.
The couple then spent around 20 minutes mingling with the crowd, receiving flowers, cards and cuddly toys from many of the school groups.
Louisa Leckie, 11, presented Kate with a giant teddy bear dressed in a Strathearn tartan kilt.
Her father Stephen said: "She was so nervous about giving it to them and was worried about being told where to stand and if she would miss them before they left.
"But they were delighted with it so she's chuffed to bits.
"It's a present for George and they said he will love it."