The tributes were visible at landmarks ranging from Edinburgh Castle to Ben Nevis, Britain's highest peak.
Other planned weekend events include a re-enactment of the coronation in Kelso and a mass picnic in Edinburgh's Princes Street Gardens.
The Queen is the first British monarch to reach the milestone.
To mark the occasion, the traditional bank holiday on the last Monday in May was moved to Thursday.
It has been followed by an extra bank holiday on Friday.
The 96-year-old monarch, who has mobility issues, has had to cancel several recent public appearances, and will not attend Friday's National Service of Thanksgiving.
But last week the Queen travelled to Balmoral in Aberdeenshire for a short break ahead of the celebrations.
The Trooping the Colour parade, to mark the Queen's official birthday, kicked things off in London and later on Thursday more than 1,500 beacons were lit across the UK and in the capital cities of the Commonwealth.
The focal point in Scotland was Edinburgh Castle where a young Army Cadet piper played Diu Regnare, a unique tune specially written for the occasion.
Lord Provost Robert Aldridge described the event as a "momentous celebration".
He added: "It is only appropriate that this unique milestone in history is marked with music.
"What more fitting location for the lighting of a beacon than from Edinburgh Castle where it can be seen from the streets below."
Elsewhere, teams from Walking With The Wounded lit beacons at the summits of Ben Nevis, Scafell Pike in England, Mount Snowdon in Wales and Slieve Donard in Northern Ireland.
Beacon events are also being held at locations including Saltcoats, North Ayrshire; Dunnottar Castle, Stonehaven; and at RAF Lossiemouth, where the celebrations featured a Military Wives Choir.
The beacons were lit simultaneously across the country at 21:45.
Among the notable local events is a re-enactment of the Queen's 1953 Coronation in Kelso in the Scottish Borders on Saturday, featuring members of the local Scouts and Guides.
Musselburgh Race Course will top off a weekend of Jubilee racing with a special corgi derby on Sunday.
A distant relative of one of The Queen's own corgis, named Paddy from Port Seton, will take part.
There will also be a performance by Louise Marshall, Scotland's national piper who was the lone piper to Her Majesty at the naming ceremony of the MS Queen Elizabeth cruise ship in 2010.
And in Kirkcudbright, Dumfries and Galloway, about 2,000 people are expected at a street party on Sunday which will see the town's St Cuthbert Street closed to traffic.
The main highlight in Edinburgh will be an open-air concert in West Princes Street Gardens on Sunday.
Members of the public are being encouraged to bring "their best picnic blankets" for the free event, which starts at 12:30.
It will feature music by the HM Royal Marines Scotland band, Love Music Community Choir and a special Edinburgh Festival Carnival parade.
The council also confirmed work has been completed on the 2022 design on the world's oldest floral clock in the gardens.
A team of five gardeners took just four weeks to plant more than 35,000 flowers and plants used to create the clock, which will be in bloom until October.
A variety of events are taking place in Scotland, including:
* Glamis Castle hosting live outdoor opera and acoustic music events in its grounds. The Queen visited the landmark during her coronation year and planted a maple tree which still stands next to one planted by her late husband, Prince Philip
* A thanksgiving service will be held at Glasgow Cathedral on Sunday
* Community lunches, street parties and afternoon teas will also take place across the country over the weekend
* Scotland's 32 local authorities have received about 100 applications to temporarily close roads to hold Jubilee parties. Thirty-two were lodged with Edinburgh Council and 25 with East Ayrshire Council.
In London, there will be a service of Thanksgiving at St Paul's Cathedral on Friday, while on Saturday there will be the Platinum Party at the Palace, which will feature acts including Sir Rod Stewart and Diana Ross.
Sunday will see the Platinum Jubilee Pageant, ending in a performance in front of Buckingham Palace.
Meanwhile, politicians have also led tributes to the record-breaking Queen.
On Wednesday, First Minister Nicola Sturgeon said had played an integral role in the story of modern Scotland,
She also confirmed the Scottish government will present The Queen with a limited edition Johnnie Walker whisky and a throw made from the tartan commissioned in honour of the three bridges across the Forth.
A Jubilee Wood of 70 native trees is also planned for planting in Holyrood Park, within sight of the Palace of Holyroodhouse.
Ms Sturgeon said: "The occasion of the Platinum Jubilee is not just about an institution. It is, above all, about the life and service of an extraordinary woman.
"Let us congratulate her warmly on a reign of unprecedented length and let us acknowledge, with deep gratitude and respect, her dedication to duty."
Scottish Secretary Alister Jack also sent his "heartfelt congratulations" to the monarch.
He added: "I know people across Scotland will join me in wishing her the very best on this huge milestone, and thanking her for her lifetime of service."