Recent developments in nonlinear optics have led to the discovery of a new class of ultrashort pulse, the `optical similariton'. Optical similaritons arise when the interaction of nonlinearity, dispersion and gain in a high-power fibre amplifier causes the shape of an arbitrary input pulse to converge asymptotically to a pulse whose shape is self-similar. In comparison with optical solitons, which rely on a delicate balance of nonlinearity and anomalous dispersion and which can become unstable with increasing intensity, similaritons are more robust at high pulse powers. The simplicity and widespread availability of the components needed to build a self-similar amplifier capable of producing optical similaritons provides a convenient experimental platform to explore the fundamental nature of dynamical self-similarity. Here, we provide an overview of self-similar pulse propagation and scaling in optical fibre amplifiers, and their use in the development of high-power ultrafast optical sources, pulse synthesis and all-optical pulse regeneration.