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.  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 now also pinpointing FRB locations and providing host galaxy associations.  More than a decade since the famous 'Lorimer burst', we are now making rapid progress in our understanding of the enigmatic FRB phenomenon.  In this talk, I will focus on how observations with the European VLBI Network (EVN) and the Low-Frequency Array (LOFAR) are shedding light on the nature of FRB sources.  These observations have provided milli-arcsecond localisations and nanosecond-resolution polarimetry to decode the source model and emission mechanism.