Newton polytope of a polynomial is the convex hull of the exponents of its monomials. Newton polytopes establish a connection between algebraic geometry and convex geometry. For instance, the number of common roots of $n$ generic polynomials on the $n$-dimensional complex torus is equal to the Minkowski mixed volume of their Newton polytopes. We recall this in detail, extend it to a certain relation between elimination theory (which is about eliminating variables in systems of polynomial equations) and Minkowski integrals (which are Riemann integrals of polyhedral-valued functions), and formulate some open questions.