  Irregular dust grains are subject to radiative torques when irradiated by
interstellar starlight. It is shown how these radiative torques may be
calculated using the discrete dipole approximation. Calculations are carried
out for one irregular grain geometry, and three different grain sizes. It is
shown that radiative torques can play an important dynamical role in spinup of
interstellar dust grains, resulting in rotation rates which may exceed even
those expected from H_2 formation on the grain surface. Because the radiative
torque on an interstellar grain is determined by the overall grain geometry
rather than merely the state of the grain surface, the resulting superthermal
rotation is expected to be long-lived. By itself, long-lived superthermal
rotation would permit grain alignment by normal paramagnetic dissipation on the
"Davis-Greenstein" timescale. However, radiative torques arising from
anisotropy of the starlight background can act directly to alter the grain
alignment on much shorter timescales, and are therefore central to the process
of interstellar grain alignment.
  Radiative torques depend strongly on the grain size, measured by a_eff, the
radius of a sphere of equal volume. In diffuse clouds, radiative torques
dominate the torques due to H2 formation for a_eff=0.2micron grains, but are
relatively unimportant for a_eff<0.05micron grains. This may provide a natural
explanation for the observation that $a_eff>0.1 micron grains in diffuse clouds
are aligned, while there is little alignment of a_eff < 0.05 micron grains. We
show that radiative torques are ineffective at producing superthermal rotation
within quiescent dark clouds, but can be very effective in star-forming regions
such as the M17 molecular cloud.
