Nikita Kalinin
This paper surveys tropical modifications, a notion that has become part of the folklore of tropical geometry. Tropical modifications are used in tropical intersection theory, tropical Hodge theory, and the study of singularities. They admit interpretations in several contexts, including hyperbolic geometry, Berkovich spaces, and non-standard analysis. The goal of the paper is to present several points of view, give references, and illustrate the usefulness of tropical modifications. We assume that the reader has already encountered tropical modifications and wants to understand them better. The paper also contains two new contributions: an obstruction to the realizability of non-transversal intersections and a tropical version of Weil's reciprocity law.