  Toric geometry provides a bridge between the theory of polytopes and
algebraic geometry: one can associate to each lattice polytope a polarized
toric variety. In this paper we explore this correspondence to classify smooth
lattice polytopes having small degree, extending a classification provided by
Dickenstein, Di Rocco and Piene. Our approach consists in interpreting the
degree of a polytope as a geometric invariant of the corresponding polarized
variety, and then applying techniques from Adjunction Theory and Mori Theory.
