Pinpointing fast radio bursts in space and time

In the past decade we have started to explore extragalactic and intergalactic space using millisecond-duration radio flashes called `fast radio bursts' (FRBs). These cosmological signals are surprisingly abundant: there is likely an FRB occurring somewhere on the sky at least once every minute. They are also unique probes of the otherwise invisible material between stars and galaxies. But what is producing them? Thanks to a new generation of wide-field radio telescopes, several FRBs per day are now being discovered. Novel high-time-resolution observations using radio interferometers are also pinpointing FRB locations and providing host galaxy associations. More than a decade since the discovery of the famous `Lorimer burst', we are making rapid progress in our understanding of the enigmatic FRB phenomenon. In this talk, I will briefly review the status of the field, highlighting some of the latest discoveries and what they have taught us. At the same time, recent discoveries are showing us that we have still only scratched the surface in terms of the vast parameter space we can potentially explore. Expanding our exploration for FRB-like signals to an even wider range of timescales, luminosities and event-rates will allow us to discover new types of extreme astrophysical phenomena - some of which are likely to have high-energy counterparts