Bidirectional transformations are ubiquitous in applied category theory, in the form of lenses, Dialectica categories, morphisms of containers, modular data accessors, and more. In particular, they provide the foundations for categorical cybernetics.
This is a somewhat technical topic. The current goal in dependent optics is to find good dependently-typed generalizations of optics, which are themselves a generalization of lenses. Optics seems to have better operational properties than lenses, and capture a wider range of bidirectional transformations.