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Fast radio bursts (FRBs) are very short and bright transients visible over extragalactic distances. Their origin is still a mystery, but since the radio pulse undergoes dispersion caused by free electrons along the line of sight, FRBs can be used to probe the distribution of baryons on cosmological scales.
In this talk I will give a brief overview of this rapidly evolving field. Recently, my collaborators and I used the small sample of currently known events to measure the Hubble constant (arxiv 2104.04538, 2301.03527), and constraints are expected to improve considerably in the near future as more and more data from the ongoing search programs becomes available. Future large FRB samples provide exciting opportunities not only to understand the physical mechanism, but also to use their dispersion to measure the cosmic baryons on largest scales and to look for new physics such as primordial non-Gaussianity (2007.04054) or deviations from the equivalence principle (2302.10072)