This one https://upload.wikimedia.org/wikipedia/commons/d/d4/Karl_Marx_001.jpg
What's the story behind it? Why isn't some other picture associated with him?
[Most of the text below is based on Scolari, 2020, who uses material from Bouvier, 2013, but I don't have access to the latter]
There are 15 known pictures of Karl Marx, which can all be seen here, taken from 1861 to 1882. The most iconic picture was part of series of 4 taken in August 1875 in London by photographer John Mayall, well-known for his portraits of Queen Victoria and of the Royal Family. Mayall had already photographed Marx in 1872, and an engraving of this earlier picture was used notably in the first French edition of Das Kapital.
Marx's increasing celebrity after the publication of Das Kapital in 1867 led to a debate in his circle of family and friends about the dissemination of his likeness. Marx was concerned and opposed to it, but Friedrich Engels still had Marx's picture published in newspapers. Marx actually liked the picture taken in Hannover by Friedrich Wunder in 1867 and wrote to his sister Laura:
I am very glad that my photogramm has met with such good reception. The shadow is at all events less troublesome than the original.
While less famous than the Mayall set, it has also been widely used, for instance in the American edition of Wage-labor and Capital of 1891.
The demand for portraits of Marx grew again after the Paris Commune of 1871, but it was after Marx's death that the Mayall photo(s) of 1875 became truly iconic. Engels disseminated 12,000 copies of them around the world, making them available to newspapers and organisations. Engels justified his choice as follows (letter to Eduard Bernstein in Zurich, 28 April 1883):
It is the last, best shot, where the Moor appears in his cheerful, victorious olympic calm.
Engels wrote in the same letter:
Mayall, the leading London photographer always to work for Marx, has the principle: WE DO NOT TAKE MONEY FROM EMINENT PEOPLE. So we can't now press the man for copies (he is extremely muddled), except by a roundabout route. Hence we have given him an order, claiming it was for a German bookseller, for 1,000 cartes de visite (£12 = M240 = 24d. each) and 200 CABINET PORTRAITS (3/4 figure) à £8 = M160 = 80d. each. […] I am offering them to you, and to Liebknecht and Sorge in New York after deducting those we need ourselves.
In another letter (1 May 1883) to Friedrich Adolf Sorge in New York, a member of the International Workers Association, Engels talked again about ordering the pictures from Mayall, adding that "If the above quantity does not suffice, no doubt we shall be able to get hold of more, but a quick decision is necessary." Photos were also sent to socialist Karl Liebknecht.
Here is a drawn version of it published in Le Monde Illustré of 31 March 1883, and the photograph itself in Karl Marx's Oekonomische Lehren (1893) by Czech-Austrian Marxist Karl Krautsky. The Marx photo that illustrates the Italian version the Wage Labour and Capital (1893) is not the iconic one but part of the same series. It is thus likely that Engels disseminated several pictures of the Mayall set.
Sources