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The first Linotype machine was built in New York by Ottmar Mergenthaler in 1886. Perhaps the world's first commercially-viable typesetting machine, Mergenthaler's invention could cast a line of type on-the-fly, greatly speeding up the process of metal typesetting. Newspapers around the world took advantage of this immediately. Newsppapers would always be the biggest users of Linotype Machines.
The Linotype Machine sparked a revolution in typesetting. Soon, competitor machines appeared on the market, like the Monotype Machine. Linotype Machines were used well into the 60s and 70s. From the late 1950s onward, however, Linotype had begun to produced photo-typesetting equipment, and later would go onto build digital machines. The typefaces that were designed for these various machines would later be sold as PostScript (and other format) fonts by a company called Linotype Library (since 2005 simply "Linotype GmbH").
The Linotype Machine was in a large part technically possible only because of Linn Boyd Benton's pantographic punchcutter.
A two-part film showing in great detail how the Linotype machine works is available online at the Prelinger Archives at archive.org. The links below will take you to a page containing information and several downloadable formats for each part: