After being awarded his PhD by MIT, he spent one year as a postdoctoral researcher at the University of California, Berkeley, and then accepted a position at Bell Labs in New Providence, New Jersey.

[21] In 2017, he received the Dirac Medal of the ICTP and for 2019 the BBVA Foundation Frontiers of Knowledge Award in Basic Sciences.

[25][26] He was elected as an ACM Fellow in 2019 "for contributions to quantum-computing, information theory, and randomized algorithms".

[28] In 2020, he was elected a member of the National Academy of Engineering for pioneering contributions to quantum computation.

[29] In an interview published in Nature on October 30, 2020, Shor said that he considers post-quantum cryptography to be a solution to the quantum threat, although a lot of engineering effort is required to switch from vulnerable algorithms.

[30] Along with three others, Shor was awarded the 2023 Breakthrough Prize in Fundamental Physics for "foundational work in the field of quantum information.