<p>Microcombs—optical frequency combs generated by nonlinear integrated microcavity resonators—have the potential to offer the full capability of their benchtop counterparts, but in an integrated footprint. They have enabled breakthroughs in spectroscopy, microwave photonics, frequency synthesis, optical ranging, quantum sources, metrology, optical neuromorphic processing and more. One of their most successful applications is in optical-fibre communications, where they have formed the basis for massively parallel ultrahigh-capacity multiplexed data transmission. Innovative approaches have been used in recent years to phase-lock or mode-lock different types of microcombs, from dissipative Kerr solitons to dark solitons, soliton crystals and others, and this has enabled their use as sources for advanced coherent modulation-format optical communications systems, which have achieved ultrahigh data capacity bit rates breaking the petabit-per-second barrier. Here we review this new and exciting field, chronicling the progress and highlighting the challenges and opportunities.</p>