  The nuclear physics relevant to the electric dipole moment (EDM) of the
deuteron is addressed. The general operator structure of the $P$- and $T$-odd
nucleon-nucleon interaction is discussed and applied to the two-body
contributions of the deuteron EDM, which can be calculated in terms of $P$- and
$T$-odd meson-nucleon coupling constants with only small model dependence. The
one-body contributions, the EDMs of the proton and the neutron, are evaluated
within the same framework. Although the total theoretical uncertainties are
sizable, we conclude that, compared to the neutron, the deuteron EDM is
competitive in terms of sensitivity to $C P$ violation, and complementary with
respect to the microscopic sources of $C P$ violation that can be probed.
