  Self-alignment describes the property of a polar active unit to align or
anti-align its orientation towards its velocity. In contrast to mutual
alignment, where the headings of multiple active units tend to directly align
to each other -- as in the celebrated Vicsek model --, self-alignment impacts
the dynamics at the individual level by coupling the rotation and displacements
of each active unit. This enriches the dynamics even without interactions or
external forces, and allows, for example, a single self-propelled particle to
orbit in a harmonic potential. At the collective level, self-alignment modifies
the nature of the transition to collective motion already in the mean field
description, and it can also lead to other forms of self-organization such as
collective actuation in dense or solid elastic assemblies of active units. This
has significant implications for the study of dense biological systems,
metamaterials, and swarm robotics. Here, we review a number of models that were
introduced independently to describe the previously overlooked property of
self-alignment and identify some of its experimental realizations. Our aim is
three-fold: (i)~underline the importance of self-alignment in active systems,
especially in the context of dense populations of active units and active
solids; (ii)~provide a unified mathematical and conceptual framework for the
description of self-aligning systems; (iii)~discuss the common features and
specific differences of the existing models of self-alignment. We conclude by
discussing promising research avenues in which the concept of self-alignment
could play a significant role.
