  Polarization arising from aligned dust grains presents a unique opportunity
to study magnetic fields in the diffuse interstellar medium and molecular
clouds. Polarization from circumstellar regions, accretion disks and comet
atmospheres can also be related to aligned dust.To reliably trace magnetic
fields quantitative theory of grain alignment is required. Formulating the
theory that would correspond to observations was one of the longstanding
problems in astrophysics. Lately this problem has been successfully addressed,
and in this review we summarize some of the most important theoretical advances
in the theory of grain alignment by radiative torques (RATs) that act on
realistic irregular dust grains. We discuss an analytical model of RATs and the
ways to make RAT alignment more efficient, e.g. through paramagnetic relaxation
when grains have inclusions with strong magnetic response. For very small
grains for which RAT alignment is inefficient, we also discuss paramagnetic
relaxation and a process termed resonance relaxation. We provide an extensive
analysis of the observational tests of grain alignment theory.
