We define and study non-abelian unipotent periods for algebraic varieties. Their calculations reduce to calculations of the monodromy of iterated integrals on algebraic varieties. We study the monodromy with some details on pointed projective lines and on configuration spaces. We give a new proof of Drinfeld-Ihara 5-cycle relation. We have also some necessary and sufficient conditions (unfortunately almost tautological) that the values of the Riemann zeta function at odd integers are irrational.