Solitons as elementary particles: a paradigm scrutinized

Solitons occur as topologically stable solutions of the classical field equations underlying a large class of quantum field theories. We review some of the results which show that these solitons behave like classical Newtonian particles, albeit with some surprising behaviour, and that, suitably quantized, these solitons contribute to the particle spectrum of the quantum field theory. Along the way, we highlight some of the remaining problems. We also comment on the reverse issue: do the elementary particles we know experimentally have a description as solitons?