  We study the problem of finding exactly marginal deformations of N=1
superconformal field theories in four dimensions. We find that the only way a
marginal chiral operator can become not exactly marginal is for it to combine
with a conserved current multiplet. Additionally, we find that the space of
exactly marginal deformations, also called the "conformal manifold," is the
quotient of the space of marginal couplings by the complexified continuous
global symmetry group. This fact explains why exactly marginal deformations are
ubiquitous in N=1 theories. Our method turns the problem of enumerating exactly
marginal operators into a problem in group theory, and substantially extends
and simplifies the previous analysis by Leigh and Strassler. We also briefly
discuss how to apply our analysis to N=2 theories in three dimensions.
