  The shapes of galaxies are not randomly oriented on the sky. During the
galaxy formation and evolution process, environment has a strong influence, as
tidal gravitational fields in the large-scale structure tend to align nearby
galaxies. Additionally, events such as galaxy mergers affect the relative
alignments of both the shapes and angular momenta of galaxies throughout their
history. These "intrinsic galaxy alignments" are known to exist, but are still
poorly understood. This review will offer a pedagogical introduction to the
current theories that describe intrinsic galaxy alignments, including the
apparent difference in intrinsic alignment between early- and late-type
galaxies and the latest efforts to model them analytically. It will then
describe the ongoing efforts to simulate intrinsic alignments using both N-body
and hydrodynamic simulations. Due to the relative youth of this field, there is
still much to be done to understand intrinsic galaxy alignments and this review
summarises the current state of the field, providing a solid basis for future
work.
