About a decade after Pearlmutter and Siskind’s pioneering work, in the wake of remarkable progress made by deep learning applications, the programming languages community has devoted a considerable amount of attention to automatic differentiation. In this talk, after a brief (and partial) survey of what has been done so far, I’d like to discuss some questions and challenges, both theoretical and related to implementation, that arise when looking at automatic differentiation from the standpoint of programming languages, inspired by ongoing work with Michele Pagani.