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Magnetic fields play a crucial role in various astrophysical processes, including star formation, accretion of matter, transport processes (e.g., transport of heat), and cosmic rays. One of the easiest ways to determine the magnetic field direction is via polarization of radiation resulting from extinction on or/and emission by aligned dust grains. Reliability of interpretation of the polarization maps in terms of magnetic fields depends on how well we understand the grain-alignment theory. Currently the grain-alignment theory is a predictive one, and its results nicely match observations. Among its predictions is a subtle phenomenon of radiative torques. after having stayed in oblivion for many years after its discovery, is currently viewed as the most powerful means of alignment. In this article, I shall review the basic physical processes involved in grain alignment, and the currently known mechanisms of alignment. I shall also discuss possible niches for different alignment mechanisms. I shall dwell on the importance of the concept of grain helicity for understanding of many properties of grain alignment, and shall demonstrate that rather arbitrarily shaped grains exhibit helicity when they interact with gaseous flows and radiative fluxes.