Carbon nanotubes (CNTs) possess both remarkable optical properties and high potential for integration in various photonic devices. We overview, here, recent progress in CNT applications in fibre optics putting particular emphasis on fibre lasers. We discuss fabrication and characterisation of different CNTs, development of CNT-based saturable absorbers (CNT-SA), their integration and operation in fibre laser cavities putting emphasis on state-of-the-art fibre lasers, mode locked using CNT-SA. We discuss new design concepts of high-performance ultrafast operation fibre lasers covering ytterbium (Yb), bismuth (Bi), erbium (Er), thulium (Tm) and holmium (Ho)-doped fibre lasers.