A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this talk we will explain the basics of the theory of computational flows and how they make a sound and complete interpretation for bounded theories of arithmetic. This property helps us to decompose a first order arithmetical proof into a sequence of computational reductions by which we can extract the computational content of the low complexity statements in some bounded theories of arithmetic such as I Delta_0, T^k_n, I Delta_0+EXP and PRA.