Topological solitons that polarize the Dirac vacuum can assume fractional fermion (and electric) charge. The effect is investigated in detail in low-dimensional [(1+1)- and (2+1)-dimensional space-time] quantum field theory models. A review is given of phenomena associated with fractional charges found experimentally in quasi-one-dimensional (spin-charge anomaly in lightly doped polyacetylene) and two-dimensional systems (quantum Hall effect). Topics covered include: (1) fractional charge in one-dimensional quantum field theory models, (2) anomalous quantum numbers in the Peierls--Fr\"ohlich system, and (3) twodimensional models of quantum field theory and the quantum Hall effect.