------------------------------------------------------------------------ `Feynman Integrals and Graph Polynomials' Abstract: The integrand of a scalar multi-loop integral in its Feynman parametric form can be expressed in terms of two graph polynomials. These polynomials play a crucial role in current techniques for the computation of Feynman integrals as well as in recent formal researches related to periods in geometry. In this talk I want to refer to both aspects. After a review of some properties of these polynomials I want to focus on the method of Sector Decomposition for the numerical computation of Feynman integrals. In this approach, the systematic manipulations on the polynomials resemble the resolution of singularities by a sequence of blow-ups in algebraic geometry. ------------------------------------------------------------------------