The undeclared war began on April 2 1982 when Argentina invaded the British overseas territory.
On June 14 of the same year, as British forces approached its capital Stanley, Argentina surrendered.
In total, 255 British servicemen, 649 Argentinian military personnel, and three civilians died, while many more were wounded.
Some who were deployed to the islands marched in Edinburgh on Saturday (June 18) before a remembrance ceremony was held.
They were joined by veterans from other conflicts, Edinburgh's Lord Provost and Cabinet Secretary Keith Brown.
A parade made its way from Charlotte Square, along George Street, to St Andrews Square.
Take a look through our picture gallery.
In total, 255 British servicemen, 649 Argentinian military personnel, and three civilians died, while many more were wounded.
5. Lord Provost and Keith Brown MSP
Lord Provost of the City of Edinburgh Robert Aldridge (left) joins Cabinet Secretary for Justice and Veterans Keith Brown MSP (right) and senior military personnel, as well as Falklands veterans and members of the wider armed forces community, to remember the 40th anniversary of the end of the conflict, during a parade and service of remembrance in Edinburgh. Photo: Jane Barlow
6. Standard Bearers
Standard Bearers, who joined military personnel, alongside Falklands veterans and members of the wider armed forces community, to remember the 40th anniversary of the end of the conflict, during a parade and service of remembrance in Edinburgh. Photo: Jane Barlow
7. The Royal Marines Band
The Royal Marines Band lead Falklands veterans and members of the wider armed forces community, during a parade and service of remembrance to remember the 40th anniversary of the end of the conflict, in Edinburgh. Photo: Jane Barlow
8. Falklands veterans
Falklands veterans and members of the wider armed forces community, remember the 40th anniversary of the end of the conflict, during a parade and service of remembrance in Edinburgh. Photo: Jane Barlow