A sharp view of fast radio bursts

Fast radio bursts (FRBs) are extremely brief and powerful flashes of radio waves originating from distant galaxies. Discovered only in 2007, they represent one of the most enigmatic phenomena in modern astronomy. While thousands are now known, their physical origin(s) remains uncertain. This thesis presents an observational study of repeating FRBs, sources that emit multiple bursts from the same location on the sky and therefore provide a unique opportunity for detailed investigation. Using archival data and new observations from some of the world's largest radio telescopes, this work focuses on two repeating sources. The thesis explores FRBs in both the time domain and the image domain. High-time-resolution analyses reveal burst durations spanning from milliseconds down to microseconds, demonstrating that FRBs can produce radio emission across a wide range of timescales and that standard search techniques miss the shortest events. High-spatial-resolution imaging using very long baseline interferometry precisely localizes FRBs within their host galaxies. We show that these sources, and other hyperactive repeating FRBs, predominately originate from low metallicity dwarf galaxies and that some of them spatially coincide with persistent radio emission. Together, these results provide new insights into the environments, progenitors and emission mechanisms of FRBs.