  This review aims at a theoretical discussion of Dirac points in
two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent
low-energy electrons in graphene (two-dimensional graphite), research on Dirac
fermions in low-energy physics has spread beyond condensed-matter systems. In
these alternative systems, a large versatility in the manipulation of the
relevant band parameters can be achieved. This allows for a systematic study of
the motion and different possible fusions of Dirac points, which are beyond the
physical limits of graphene. We introduce the basic properties of Dirac
fermions and the motion of Dirac points here and aim at a topological
classification of these motions. The theoretical concepts are illustrated in
particular model systems.
