Fifty years ago, the concept of solitons in optical fibres was proposed numerically by F. Tappert and A. Hasegawa from Bell Labs. Seven years later in 1980, experiments confirmed that dispersion and the Kerr nonlinearity could combine to yield a coherent ultrashort pulse able to propagate without distortion. The implications of this discovery go well beyond the sector of telecommunications as initially suggested, and solitons now play a major role in modern ultrafast nonlinear photonics.