  We analyze the structure of multiloop supergraphs contributing to the
effective Lagrangians in 4d supersymmetric gauge theories and in the models
obtained from them by dimensional reduction. When d=4, this gives the
renormalization of the effective charge. For d < 4, the low-energy effective
Lagrangian describes the metric on the moduli space of classical vacua. These
two problems turn out to be closely related. In particular, we establish the
relationship between the 4d nonrenormalization theorems (in minimal and
extended supersymmetric theories) and their low--dimensional counterparts.
