Messud, J., 2020. Generalization of Kirchhoff reflectivity to go beyond modelling and inversion of first-order reflection data - a theoretical review. Journal of Seismic Exploration, 29: 477-504. I emphasize the connections and differences between Kirchhoff and Born modelling. I seize the opportunity to clarify aspects related to possibly non-smooth propagating media and the linearity approximation on reflectors. I discuss how they lead to a general expression for the conversion of a velocity perturbation into a reflectivity through the “generalized reflectivity' concept. The latter offers opportunities: On FWI approaches that include a reflectivity or least squares migration approaches that can be based on Kirchhoff or Born modelling: to rigorously convert the reflectivity into a velocity perturbation. In the framework of traditional Kirchhoff modelling scheme: to model first-order effects that go beyond first-order reflections (like first-order diffractions). In the framework of traditional Kirchhoff inversion or true amplitude migration, i.e., for the interpretation of seismic-migrated images: to give a basis to interpret by AVA (amplitude versus angle) more information than the amplitudes associated to first-order reflections, for instance the amplitudes of first-order diffractors. Also, it would theoretically allow to go beyond AVA analysis, inverting for the whole seismic image amplitude information (not only amplitude information at peaks) to recover the related velocity model perturbation. This is discussed formally in the article.