  We analyze spin transport in insulating antiferromagnets described by the XXZ
Heisenberg model in two and three dimensions. Spin currents can be generated by
a magnetic-field gradient or, in systems with spin-orbit coupling,
perpendicular to a time-dependent electric field. The Kubo formula for the
longitudinal spin conductivity is derived analogously to the Kubo formula for
the optical conductivity of electronic systems. The spin conductivity is
calculated within interacting spin-wave theory. In the Ising regime, the XXZ
magnet is a spin insulator. For the isotropic Heisenberg model, the
dimensionality of the system plays a crucial role: In d=3 the regular part of
the spin conductivity vanishes linearly in the zero frequency limit, whereas in
d=2 it approaches a finite zero frequency value.
