  In this paper we present the complete expressions of the lepton and neutron
electric dipole moments (EDMs) in the Standard Model Effective Field Theory
(SMEFT), up to 1-loop and dimension-6 level and including both RG running
contributions and finite corrections. The latter play a fundamental role in the
cases of operators that do not renormalize the dipoles, but there are also
classes of operators for which they provide an important fraction, $10-20\%$,
of the total 1-loop contribution, if the new physics scale is around
$\Lambda=5$ TeV. We present the full set of bounds on each individual Wilson
coefficient contributing to the EDMs using both the current experimental
constraints, as well as those from future experiments, which are expected to
improve by at least an order of magnitude.
