Walter studied at the Bauhaus in Dessau with Josef Albers, Wassily Kandinsky, Paul Klee and Joseph Schmidt. After finishing his studies he moved to Paris, where he worked with Jean Carlu, A.M. Cassandre and Man Ray. He was the Paris editor of the Swiss magazine Graphis and founder/editor of the International Poster Annual and Posters. He emigrated to the US in 1949, and became a freelance designer for many US companies and organizations. He joined the staff of Fortune magazine in 1951 and was the art director of the magazine from 1962–74; he designed 79 covers. Allner taught at Parsons School of Design 1974–86 and was visiting lecturer at many other schools. In 1972 he was elected President of the US chapter of AGI and in 1974 was elected International President (the first from the US). He was the recipient of the Bauhaus Dessau medal from the German Academy of Architecture and the AGI Henri statuette for a lifetime of outstanding achievement in graphic design.