Nonesuch Press's first book, a volume of John Donne's Love Poems was issued in May 1923. In total, it produced more than 140 books. The press was at its peak in the 1920s and 1930s, but continued operating through the mid-1960s. During the late 1930s and throughout the 1940s, Meynell ceded control of the Press to George Macy, founder and owner of the Limited Editions Club. In the early 1950s, however, Meynell united with the owner of The Bodley Head, Max Reinhardt, and resumed control of Nonesuch. During the final years of the Press's existence, its remit was extended to include editions of classic children's books, such as E. Nesbit's The Treasure Seekers and Andrew Lang's fairy tales (these formed part of the Press's Cygnet impression).
Nonesuch was unusual among private presses in that it used a small hand press to design books (an Albion), but had them printed by commercial printers: for example, the Kynoch Press based in Birmingham. The purpose of this method was to produce book designs with the quality of a fine-press but available to a wider audience at lower prices. Meynell also wanted to demonstrate that "mechanical means could be made to serve fine ends. He believed that the production of exquisitely designed and produced books was not the preserve of the private press predicated upon the example established by William Morris's Kelmscott Press, which emphasized the primacy of the handpressed book.
Among the press's best-known editions were the collected works of William Congreve and William Wycherley and translations of Cervantes and Dante. A number of illustrated editions were also produced. Nonesuch's editions are prized by collectors; particularly rare and well-designed editions can sell for more than £1000 ($1774 U.S.).
In November 2005, Barnes and Noble issued reprints of the Nonesuch editions of Charles Dickens's novels, including Bleak House, Great Expectations and Hard Times, the Christmas Books, David Copperfield, Oliver Twist, and Nicholas Nickleby. Nonesuch editions have also been republished by Duckworth.