The study of toric varieties is a wonderful part of algebraic geometry. There are elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology. Toric varieties also have unexpected applications in areas as diverse as physics, coding theory, algebraic statistics, and geometric modeling. Moreover, as noted by Fulton [105], "toric varieties have provided a remarkably fertile testing ground for general theories.
Source: wiktionary