Following the flashes Monitoring and localising repeating fast radio bursts

Fast radio bursts (FRBs) are millisecond-duration flashes of coherent radio emission originating from extragalactic distances. While thousands of sources have been discovered, their origins remain enigmatic. Some FRB sources are known to emit bursts repeatedly. The recurrent activity seen in these repeaters, allow for long-term monitoring to study the evolution of burst properties, and precise localisation to identify their host galaxies and local environments. This thesis presents the results of long-term monitoring of two repeaters and two very-long-baseline interferometry (VLBI) localisations. The first known repeater, FRB 20121102A, was observed with the Arecibo telescope for a year. Hundreds of bursts were detected during a month-long burst storm. These observations revealed diverse burst morphologies and hinted that non-repeater bursts may be the most energetic, rare events from repeating sources. FRB 20220912A, a hyperactive source, was monitored with the Nançay Radio Telescope shortly after a seemingly spontaneous awakening. Nearly 700 bursts were detected and analysis of them provided quantitative criteria for models of (hyperactive) repeaters. Approximately 1% of the bursts also displayed dense clusters of microshots - broadband pulses lasting tens of microseconds. These microshots were superimposed on broader emission components that still exhibited time-frequency drifting, potentially suggesting different emission mechanisms. Using the European VLBI Network, subarcsecond localisations were achieved for two sources. FRB 20220912A was determined to be closer to the center of its host galaxy than expected, with no associated persistent radio emission, despite its hyperactivity. Meanwhile, FRB 20190208A was localised to the lowest luminosity host galaxy to date, highlighting the need for both precise localisation and deep optical imaging for robust host associations.