Understanding, counting, and finding the solutions of a system of polynomial equations is a classical and in general hard problem. However, many such systems consist of sparse polynomials, which means that not all monomials up to a certain degree actually occur in the polynomials. The concrete sparsity structure of such a system can be encoded in a tuple of so-called Newton polytopes and understanding the properties of such a tuple yields important insights about the system itself. Such insights can for example vastly simplify the task of finding solutions to a system. The scope of this project was to study different properties of tuples of Newton polytopes from the point of view of a mixed lattice polytope theory and to apply our findings in order to answer several questions from algebraic geometry.