Lattice polytopes (that is, polytopes with integer-coordiante vertices) are important both in Algebraic Geometry (toric geometry, commutative algebra, singularities) and Optimization (integer programming). In particular some attention has been devoted to triangulations of them and, most particularly, to the existence or not of unimodular triangulations for various families of them. In this talk I’ll try to survey what is known about triangulations of lattice polytopes, with an excursion into the classification of low-dimensional empty simplices, that is, lattice simplices with no lattice points other than their vertices. Empty simplices are important since they are the ``building blocks’’ in to which every lattice polytope can be triangulated.