W.M. Conway was educated at Repton and Trinity College, Cambridge, where he studied mathematics and became a close friend of Karl Pearson. He became interested in early printing and engraving, and in 1880 made a tour of the principal libraries of Europe in pursuit of his studies, the result appearing in 1884 as a History of the Woodcutters of the Netherlands in the Fifteenth Century. His later works on art included:
From 1882 to 1885, Conway was a Cambridge University extension lecturer. He climbed extensively in the Alps as an undergraduate, and was elected to the Alpine Club in 1877. (He was president from 1902 to 1904.)
In 1881 he published the Zermatt Pocketbook, the model for a series of Conway and Coolidge's Climbers' Guides, which he edited with W. A. B. Coolidge. Conway was responsible for many beautiful mountain names, such as Wellenkuppe, Windjoch, and Dent du Requin.
From 1884 to 1887 Conway was Professor of Art at University College, Liverpool; and from 1901 to 1904 he was Slade Professor of Fine Arts at Cambridge University. He was knighted in 1895 for his efforts in mapping 5,180 square km of the Karakoram Range in the Himalayas three years earlier.
In 1892, in the course of an exploring and mountaineering expedition undertaken under the auspices of the Royal Society, the Royal Geographical Society and the British Association, he made an ascent of a subsidiary summit of Baltoro Kangri, claiming a world altitude record with a height of 23,000 ft (7,010 m). However, subsequent measurements have revised his height to 22,322 ft (6,501 m). In 1896-1897 he explored the interior of Spitsbergen, and the following year he explored and surveyed the Bolivian Andes, climbing Sorata (21,500'/6,553m) and Illimani (21,200'/6,461m). He also ascended Aconcagua (22,831'/6,959m) and explored Tierra del Fuego. At the Paris exhibition of 1900 he received the gold medal for mountain surveys, and the founders medal of the Royal Geographical Society in 1905, and served as President of the Alpine Club for 1902-1904. His expeditions are described in:
Conway had been involved in politics for some time, consorting with both major parties allegedly in pursuit of a knighthood and a barony; he received both. He was elected Unionist Member of Parliament for the Combined English Universities in 1918, serving until 1931. He was raised to the peerage as 1st Baron Conway of Allington. This title became extinct on his death.
Conway was founder and first Director-General of the Imperial War Museum and a trustee of the National Portrait Gallery. His photograph collection formed the basis of the Conway Library at the Courtauld Institute of Art in London. He was also responsible for the restoration of Allington Castle
Another of Conway's interests was woodcuts and early printed books. This was encouraged by the Cambridge University Librarian, Henry Bradshaw, who financed the journeys on which Conway collected the material for ‘’Woodcutters of the Netherlands in the Fifteenth Century’’ (1884), the most learned of his thirty books. While touring art galleries in Italy in 1883, Conway met Katrina, the only child of Charles Lambard, of Augusta, Maine, builder of the Chesapeake and Ohio Railway, and stepdaughter of Manton Marble, an investor and former editor and owner of the New York World. Conway was already engaged to Rose Shakespear, but he broke this engagement, ostensibly on religious grounds, and married Katrina at Marble's home, 532 Fifth Avenue, New York, on 10 June 1884. Supported by Katrina's family, the couple moved to Park Street, London, where their only child, Agnes, was born on 2 May 1885.
In 1924 Conway began a love affair with Monica Hadow, a divorcee forty-four years his junior with whom he worked, but this ended when she remarried in 1930. When his wife, Katrina, died on 22 November 1933, she left her estate, including Allington Castle, to their daughter, although Conway continued to live there and at Westminster. On 17 November 1934, he married Iva, daughter of Daniel Christian and widow of Reginald Lawson, of Saltwood Castle, Kent. He died at the Empire Nursing Home, Vincent Square, London, on 19 April 1937, and a memorial service was held on 23 April at St Margaret's, Westminster.
Conway died in London at the age of 81. His autobiography of 1932 is called Episodes in a Varied Life, while 1914's The Sport of Collecting explains his passion for collecting artworks, photographs, etc.
For a biography see The Conways by Joan Evans.