Born in Pozsony (now Bratislava), Dohnányi was taught by his father and the local church organist. One might expect a talented Hungarian of the time to head for a more renowned centre of culture; Budapest was not such, but Dohnányi chose to study there, and in doing so inspired his schoolfriend Bartók to do so. He studied piano and composition, graduating and making his concert debut in 1897. The following year he was taken to London by Richter; already composers such as Brahms had taken notice of his compositions, and his Op. 5 Piano Concerto won the Bösendorfer Prize in 1899.
Dohnányi spent the years from 1905 to 1915 in Berlin, where he formed a close association with Joachim and earned a professorship at the Hochschule. He returned to Hungary with evangelical zeal, giving around 120 concerts every season of programmes designed to bring worthy works to the attention of the public. He taught at the Budapest Academy, and despite political upheaval he achieved much. Concert tours of America were undertaken yearly between 1921 and 1927, and at home his standing steadily grew.
During the rise of fascism Dohnányi fought to keep Jewish musicians in his orchestra and to avoid any discriminatory policies in the institutions he represented. However the situation became intolerable and he resigned from the Academy in 1941. Despite this, many felt that his actions during the war were not all they could have been, and the force of nebulous rumour led to a tour of England and eventual relocation in Tallahassee, where he became professor of music at Florida State University. The persistent, though unformed, accusations dogged his attempts to return to performance, but his recitals were well received and he was recording at the time of his death.