This talk explores the cross fertilization between number theory and superstring perturbation theory. I will first discuss multiple zeta values and their relations from the viewpoint of iterated integrals on a genus zero surface. They enter the alpha' expansion of superstring tree amplitudes in a pattern that can be understood in terms of their generating series and Hopf algebra structures. We will conclude with a glimpse of iterated integrals on a torus which give rise to elliptic analogues of multiple zeta values and find a natural appearance in one-loop amplitudes of the open superstring.
