Geodesic
Newton polytopes and tropical geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 1, pp. 91-175

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The practice of bringing together the concepts of ‘Newton polytopes’, ‘toric varieties’, ‘tropical geometry’, and ‘Gröbner bases’ has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts. Bibliography: 68 titles.
Keywords: family of algebraic varieties, Newton polytope, ring of conditions, toric variety, tropical geometry, mixed volume, exponential sum. 
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B. Ya. Kazarnovskii; A. G. Khovanskii; A. I. Esterov. Newton polytopes and tropical geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 1, pp. 91-175. http://geodesic.mathdoc.fr/item/RM_2021_76_1_a2/