Various aspects of Feynman integrals, regularization and renormalization are reviewed. Following Bloch, the focus is upon a linear algebraic approach to the Feynman rules. Using resolution of singularities, several renormalization methods are brought together. In the second part, the work of Belkale and Brosnan resp. Bloch, Esnault and Kreimer on the motivic nature of Feynman integrals is briefly sketched.