  While the problem of grain alignment was posed more than 60 years ago the
quantitative model of grain alignment that can account for the observed
polarization arising from aligned grains has been formulated only recently. The
quantitative predictions of the radiative torque mechanism, which is currently
accepted as the dominant mechanism of grain alignment, open avenues to tracing
magnetic fields in various astrophysical environments, including diffuse and
dense interstellar gas, molecular clouds, circumstellar environments, accretion
disks, comet tails, Zodiacal dust etc. At the same time, measurements of the
absolute value of polarization and its variations can, in addition, provide
unique information about the dust composition and dust environment. In the
review I describe the analytical model describing well radiative torques acting
on irregular grains and discuss how the alignment induced by radiative torques
varies in the presence of superparamagnetic inclusions and pinwheel torques,
e.g. arising from the molecular hydrogen formation over grain surface. I also
describe observations that can establish whether grains are superparamagnetic
and whether recoils from molecular hydrogen formations are powerful enough to
give rise to substantial uncompensated torques. Answering to these questions
should allow for reliable modeling of astrophysical polarization with numerous
important applications, from accounting for dust contribution in Cosmic
Microwave Background polarization studies to obtaining magnetic field strength
using Chandrasekhar-Fermi technique.
