  We classify ${\cal N}=1$ gauge theories with simple gauge groups in four
dimensions which possess a conformal manifold passing through weak coupling. A
very rich variety of models is found once one allows for arbitrary
representations under the gauge group. For each such model we detail the
dimension of the conformal manifold, the conformal anomalies, and the global
symmetry preserved on a generic locus of the manifold. We also identify, at
least some, sub-loci of the conformal manifolds preserving more symmetry than
the generic locus. Several examples of applications of the classification are
discussed. In particular we consider a conformal triality such that one of the
triality frames is a $USp(6)$ gauge theory with six fields in the two index
traceless antisymmetric representation. We discuss an IR dual of a conformal
$Spin(5)$ gauge theory with two chiral superfields in the vector representation
and one in the fourteen dimensional representation. Finally, an extension of
the conformal manifold of ${\cal N}=2$ class ${\cal S}$ theories by conformally
gauging symmetries corresponding to maximal punctures with the addition of two
adjoint chiral superfields is commented upon.
