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Mode-locked fibre lasers are important sources of ultrashort pulses, where stable pulse generation is achieved through a balance of periodic amplitude and phase evolutions. A range of distinct cavity pulse dynamics have been revealed, arising from the interplay between dispersion and nonlinearity in addition to dissipative processes such as filtering. This has led to the discovery of numerous novel operating regimes, offering significantly improved laser performance. In this Topical Review, we summarise the main steady-state pulse dynamics reported to date through cavity dispersion engineering, including average solitons, dispersion-managed solitons, dissipative solitons, giant-chirped pulses and similaritons. Characteristic features and the stabilisation mechanism of each regime are described, supported by numerical modelling, in addition to the typical performance and limitations. Opportunities for further pulse energy scaling are discussed, in addition to considering other recent advances including automated self-tuning cavities and fluoride-fibre-based mid-infrared mode-locked lasers.