Allen studied at, variously, the Art Institute of Chicago (1937-41), the School of Design, Chicago (1941), Life Magazine Photography School for the Armed Forces (1942), and the University of Chicago (1948-54). He has been influenced by the works of Atget, Edward Weston, Ansel Adams, Walker Evans and Berenice Abbott.
Retired in 1977, Allen was a professor, prior to then, at the School of the Art Institute of Chicago (1948-60 and 1966-77). He received an honorary Doctor of Fine Arts degree from the Art Institute in 1979. In 1978, at the Second Annual Chicago Art Awards, he received the "Special Artist Award: Body of Work." In 1971 the educator was awarded the Frederick Latimer Wells Professorship at the Art Institute.
Allen does documentary work with a 4 x 5 view camera. He concentrates on historical architecture and, in his words, has "the most extensive documentation of Egyptian-style American architecture in existence."