  An introductory overview of current research developments regarding solitons
and fractional boundary charges in graphene nanoribbons is presented. Graphene
nanoribbons and polyacetylene have chiral symmetry and share numerous similar
properties, e.g., the bulk-edge correspondence between the Zak phase and the
existence of edge states, along with the presence of chiral boundary states,
which are important for charge fractionalization. In polyacetylene, a fermion
mass potential in the Dirac equation produces an excitation gap, and a twist in
this scalar potential produces a zero-energy chiral soliton. Similarly, in a
gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can
produce soliton states. In polyacetylene, a soliton is bound to a domain wall
connecting two different dimerized phases. In graphene nanoribbons, a
domain-wall soliton connects two topological zigzag edges with different
chiralities. However, such a soliton does not display spin-charge separation.
The existence of a soliton in finite-length polyacetylene can induce formation
of fractional charges on the opposite ends. In contrast, for gapful graphene
nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges
induces integer boundary charges. The presence of disorder in graphene
nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the
average edge charge of gap states with energies within a small interval is e/2,
with significant charge fluctuations. However, midgap states exhibit a
well-defined charge fractionalization between the opposite zigzag edges in the
weak-disorder regime. Numerous occupied soliton states in a disorder-free and
doped zigzag graphene nanoribbon form a solitonic phase.
