The Newton polytope of a polynomial f(x,y) = Σ c_{ij} x^i y^j is the convex hull of the set of exponent vectors {(i,j) : c_{ij} ≠ 0} in ℝ². It encodes the essential combinatorial structure of f independently of coefficients. The BKK theorem (Bernstein-Khovanskii-Kushnirenko, 1975) states that the number of common zeros of n generic polynomials in (ℂ*)^n equals the mixed volume of their Newton polytopes — a vast generalization of Bezout's theorem. Newton polytopes control tropical geometry, determine asymptotic behavior of solutions, and underlie modern algorithms for solving polynomial systems.