Millions of photographs have been taken of the impressive City Chambers, and of the statues dotted around the square.
But unless you look very closely it is unlikely you will notice a memorial to one of the most horrific wartime events of the 20th century.
And it is even less likely that the average Glaswegian would know the connection between it and the city's favourite sculptor George Wyllie.
Embedded into the grey asphalt directly in front of the Cenotaph in George Square is a small bronze plaque.
It was put there by the City Council in 1985, the 40th anniversary of the dropping of atomic bombs on the Japanese cities of Hiroshima and Nagasaki as the Second World War drew to a close.
The plaque is inscribed with the words: "1985. This plaque was laid by the City of Glasgow District Council to commemorate the 40th anniversary of the loss of civilian lives caused by the dropping of the first Atomic Bombs on the cities of Hiroshima 6 August 1945 and Nagasaki 9 August 1945."
The bomb that hit Hiroshima killed 140,000 people and left thousands of others disfigured. It destroyed 70,000 of 76,000 houses in the city.
In Nagasaki 70,000 people perished. America's decision to drop the bombs was questioned in many quarters, even though a war was still going on.
Glasgow's traditional radicalism has meant the city has always had a sceptical attitude towards war so it is perhaps no surprise to find a memorial to those killed by the bombs.
So what is the connection with George Wyllie, the sculptor who gave us the Straw Locomotive, Paper Boat and Clyde Clock statues?
In 1945 Wyllie was stationed on a Navy ship in the Pacific and within weeks of the bombings, he and his shipmates were in Hiroshima witnessing the devastation.
To celebrate the 50th anniversary of the bombs, Wyllie turned George Square into a commemorative garden.
In a letter at the time Wyllie wrote: Our ship was in the Northern Pacific when the news of the bombing of Hiroshima came over the radio. About two months later I visited Hiroshima with some shipmates. At that time the idea of being 'anti-nuclear' did not exist. Radiation did not occur to us nor were we warned. Such was the innocence, ignorance and stupidity.
"We wandered amongst the exposed grid of the streets, rubbed heat - pulverised granite through our fingers, collected globules of molten glass and saw charred tree trunks everywhere. Scarred children played quietly.
"The difference of Hiroshima is that for the first time ever the evolution and eternity of this Planet and its Human Race can be converted from FERTILITY to STERILITY by a touch on an idiot button."