Ugo Fano earned his doctorate in mathematics at the University of Turin in 1934, under Enrico Persico, with a thesis entitled Sul Calcolo dei Termini Spettrali e in Particolare dei Potenziali di Ionizzazione Nella Meccanica Quantistica (On the Quantum Mechanical Calculation Spectral Terms and their Extension to Ionization). As part of his PhD examination he also made two oral presentations entitled: Sulle Funzioni di Due o Più Variabili Complesse (On the functions of two or more complex variables) and Le Onde Elettromagnetiche di Maggi: Le Connessioni Asimmetriche Nella Geometria Non Riemanniana (Maggi electromagnetic waves: asymmetric connections in non-Riemannian geometry). In 1939, Ugo Fano married Camilla Lattes, also known as Lilla, a teacher who would collaborate with him in a well-known book on atomic and molecular physics, Physics of Atoms and Molecules (1959). Appendix III of this book presents an elementary description of the collision of two charged particles, which was used by Richard Feynman in lectures that have been published as Feynman’s Lost Lecture: Motion of Planets Around the Sun. An expanded version of this book was subsequently published as Basic Physics of Atoms and Molecules (1972).

Later that year, Ugo Fano immigrated to the United States due to increasing antisemitic measures taking effect in Italy. His initial work in the U.S. was on bacteriophages and pioneering work in the study of radiological physics, specifically, the differences in the biological effects of X-rays and neutrons. After serving a stint at the Aberdeen Proving Ground during World War II, he joined the staff of the National Bureau of Standards (NBS, now the National Institute of Standards and Technology), where he was hired as the first theoretical physicist on the NBS staff. He served there until 1966, when he joined the faculty of physics at the University of Chicago. There he trained, until the early 1990s, about thirty graduate students and postdoctoral research associates, many of whom now occupy leading positions in theoretical atomic and molecular physics in the United States, Europe, and Japan.